In the United States, full-time employees (not contractors) must be paid a minimum wage per hour. Assuming both parties agree to it, are they legally allowed to be paid in goods and services equal to or greater than the minimum wage?
For example, if a restaurant worker earns a $7.25 minimum wage, would it be legal for another worker to be paid in $7.25 worth of food per hour?
As described, no.
Paying employees with benefits instead of money is called in kind remuneration. There are various limits on in kind payments around the world, including the US. Very generally, in kind payments are only allowed for particular industries and occupations, only allowed up to a certain dollar value, and only allowed as a certain fraction of the employee's wages. Furthermore, the value of the benefit can't exceed the actual cost to the employer - a meal that's priced at $7.25 on the menu is sold at a profit, and would be worth less than the menu price as in kind remuneration.
So, given the scenario described, a restaurant employer could not replace 100% of their employee's wages with food sold for the same amount. It's too high a percentage of the wage paid as in kind payment, and the menu price equivalent of the wage would not have sufficient in kind value.
A more detailed description of in kind payment laws can be found here. It's a rather long document that's not particularly well-organized, and is structured by describing various aspects of law in different geographic locations, rather than describing all aspects of the law in a location-specific manner. I was able to find US-specific law by searching the document for "United States".
The closest you will find in the United States is tip wages, which is a lower than minimum wage pay as you described and the origin of the employer benefits system, which is gifted goods to get around a pay cap.
In the first example, most minimum wage laws allow employers to pay employees (usually waitstaff in restruants) less than minimum wage provided they are making tips in excess of minimum. Normally this amounts to $2.75 in minimum wages, plus all tips made while on the clock. While this wage seems low, keep in mind Americans are very generous tippers, and tips of 20% of the bill are usually given for service (considered really good tip). Servers usually have to personally insult the guest gravely to their face to justify not even leaving a tip in the States... and even then, it's debatable. At a moderately priced resturant, it's easy for the tip to get close to $20 for a meal for five people. A waiter can easily clear $300 in hours on the job depending on how busy and how quickly they can move the customers through a meal.
The employer benifits system in the U.S. is more archaic, but in the post world war II boom in the states, the U.S. still imposed pay caps on what an employer could pay his employee. The result of this was a lot of hardworking, returning vets were not payed what their employer felt they were due, so the benefits system was a sort of cheat around the restrictions on pay raises. Essentially, the employer would buy medical and dental packages for the employee (and his family) that would cover the difference in value. Because this wasn't "paying" and allowed the employee to keep more of his take home pay, it became popular with the public (though the modern system isn't run exactly like this, most salary workers will still take a slight pay cut if they knew that the company plan was worth it. Less shopping around for themselves). It also had a benefit to employers as they didn't have to worry about employees without health care taking frequent sick days for his own health and family.
As a side note, a similar dodge for the pay cap rule had some hilarious results in Korea when it was implemented. There exists some factories that are on the border between North and South Korea that lie in the south and use northern labor but are owned by southern owners to this day (I don't know how it happened but it happened). Pay caps were placed on the norhtern work force by North Korea. This was a problem for owners as their southern workers would get annual bonus for good work but there was no way to pay Northerns and they felt really guilty... Until they realized that gifts were still allowed, Northerns typically never had enough food, and they had a sweet tooth to boot. Enter the Moon Pie! South Korean employers eventually payed their northern employees' bonuses in Moon Pies. As any nutrtionist or economist will tell you, the amount of moon pies equal to a nice bonus check is a bit beyond the ability for any human to eat by themselves... so once their families were fed, the factory workers found another use for the moon pie: the de jure official currency of North Korea's black market, which is extensive. And while I don't claim to be an economist, it doesn't take a degree in the field to see the inherint problem in North Korea that was caused by a snack replacing your printed money as the medium of trade, which certainly makes this instance one of the funniest economic crises to hit any nation. It was so bad, that North Korea had to eventually impose a limit of five pies a minimum and ended up making their own brand for domestic consumption (no word yet if there's a mint flavor offering, but the pun writes itself). South Koreans were disappointed by this turn... but this too soon passed when someone realized that "hey, you know they just sell surplus weather balloons" and brought the concept of "floating currency" to North Korea... in a rather literal definition of the meaning. This isn't helping the answer, but I can't help discuss this when talking about employer benefits as dodges to pay caps.
