maryland
The question does not specify a jurisdiction, so I choose to examine the matter for the state of Maryland, in the US. Even if that proves not to be the OP's preferred jurisdiction, this may be of use to others.
In Maryland, at least, including fish products in dishes labeled as "vegetarian" would quite probably be illegal. Specifically, it would be a deceptive trade practice. It might also be fraud.
Maryland commercial law, section 13-301 provides that:
Unfair, abusive, or deceptive trade practices include any:
False, falsely disparaging, or misleading oral or written statement, visual description, or other representation of any kind which has the capacity, tendency, or effect of deceiving or misleading consumers;
Representation that:
2.i. Consumer goods, consumer realty, or consumer services have a sponsorship, approval, accessory, characteristic, ingredient, use, benefit, or quantity which they do not have; ...
2.iv. Consumer goods, consumer realty, or consumer services are of a particular standard, quality, grade, style, or model which they are not; ...
Failure to state a material fact if the failure deceives or tends to deceive;
...
Deception, fraud, false pretense, false premise, misrepresentation, or knowing concealment, suppression, or omission of any material fact with the intent that a consumer rely on the same in connection with:
9.i. The promotion or sale of any consumer goods, consumer realty, or consumer service;
Restaurant food, including take-out food, is pretty clearly consumer goods. Listing a dish as "vegetarian" would be a representation that might well be materiel to a particular customer. Doing so falsely would be deception. Failing to mention the presence of fish products would be "knowing concealment" and "Failure to state a material fact", and would have a tendency to mislead customers.
The US District court, intercepting this statute in THOMAS HIBDON, ET AL v. SAFEGUARD PROPERTIES, LLC., ET AL. (2015), wrote:
In other words, it is not ordinarily the one time (or even necessarily the repeated) occurrence of an act that suffices to constitute the statutory tort of “unfair trade practice.” These may all be isolated events. Rather, it is the “common” procedure, possibly “formally adopted,” “repeated or customary,” “the usual way” that, consistent with the Legg analysis, transforms the conventional tort into the statutory tort of “unfair trade practice.” (page 14 of the posted PDF decision)
Thus regularly describing as "vegetarian" dishes that are not would constitute a "practice" under this law.
In addition, such actions might constitute ordinary fraud. According to this article from a law office
In Maryland, to establish a claim of fraudulent misrepresentation, a plaintiff must prove: (1) that a false representation was made, (2) that its falsity was either known or that the representation was made with such reckless disregard to the truth as to be equivalent to actual knowledge of falsity, (3) that the representation was made for the purpose of defrauding the plaintiff, (4) that the plaintiff had the right to, and did, reasonably rely on the representation, and would not have acted had the misrepresentation not been made, and (5) that the plaintiff suffered damage directly resulting from the misrepresentation. See Swinson v. Lords Landing Village Condo., 360 Md. 462, 476, 758 A.2d 1008, 1016 (2000) (citing Gittings v. Von Dorn, 136 Md. 10, 15-16, 109 A. 553, 553-54 (1920); Martens Chevrolet v. Seney, 292 Md. 328, 333, 439 A.2d 534, 537 (1982))
It is at least possible that a knowingly false menu description of a dish would fit that definition. It is (1) false, (2) known to be false (3) intended to induce customers to buy, and (4) it is reasonable for a patron to rely on the restaurant's printed description of a dish. As to damages, that would depend on the specific facts.
This leaves uncertain whether "vegetarian", in Maryland, would be held to exclude fish or fish products. As mentioned in the comment by user Nij, in some cultures this is not so, and I could find no case clearly on point.
Merriam-Webster defines "vegetarian" (adjective, sense 2) as:
not containing meat : consisting wholly of vegetables, fruits, grains, nuts, and sometimes eggs or dairy products.
Cambridge gives sense B1 as:
not eating or including meat: The restaurant's very good for fish, but I'd give their vegetarian options a miss. (one example out of several)
the urban Dictionary gives:
Someone who does not eat meat. This includes fish and poultry, although some people claim to be 'modified vegetarians' and will eat these.
Collins dictionary gives:
Vegetarian food does not contain any meat or fish.
All these are ordinary dictionary definitions, not strictly legal definitions. But courts often turn to dictionary defs in stuatory construction. Indeed in THOMAS HIBDON, ET AL v. SAFEGUARD PROPERTIES, LLC., ET AL. (linked above) footnote 6 says:
A dictionary definition may provide a “useful starting point,” though not a dispositive answer, in determining a statute's meaning. See Blue v. Prince George’s Cnty., 434 Md. 681, 690 n.12 (2013).
If, in light of such definitions and other evidence that might be offered in an actual case, the reasonable expectation of the customer is that fish are excluded from "vegetarian", and the merchant knew or should have known that, the customer might prevail. This is not a final answer, but at least it indicates the applicable legal framework. A key question is, I think, whether the presence of fish is a "materiel fact". (And, of course, if fish were in fact present.)
If, as a comment suggests, a dish is labeled both "vegetarian" and "fish" or "shrimp" or some similar term, it would be far less reasonable for a patron to claim to have been misled.
There is also the question of a measure of damages. If the damage is only the price of an unwanted meal, it may well be too small for a suit to make economic suit, even in a small claims court. There might be cases where greater damages would be available.
