No, it is not
A mutual fund holding, whether in an index fund, or a managed fund, is not considered to be a "financial interest" in the underlying stocks or companies, and does not require that a judge be disqualified. See details below.
However, if the holding is sizable, and the case so impacts the company that the probable impact on the judge's financial position would be substantial, then the rule against an "appearance of impropriety" might apply.
Cannon 2 of the Code of Conduct for United States Judges says:
(B) Outside Influence. A judge should not allow family, social, political, financial, or other relationships to influence judicial conduct or judgment. A judge should neither lend the prestige of the judicial office to advance the private interests of the judge or others nor convey or permit others to convey the impression that they are in a special position to influence the judge.
Cannon 3 (C) (1) says:
(1) A judge shall disqualify himself or herself in a proceeding in which the judge’s impartiality might reasonably be questioned, including but not limited to instances in which:
(c) the judge knows that the judge, individually or as a fiduciary, or the judge’s spouse or minor child residing in the judge’s household, has a financial interest in the subject matter in controversy or in a party to the proceeding, or any other interest that could be affected substantially by the outcome of the proceeding;
Cannon 3 (C) (2) says:
(2) A judge should keep informed about the judge’s personal and fiduciary financial interests and make a reasonable effort to keep informed about the personal financial interests of the judge’s spouse and minor children residing in the judge’s household.
Cannon 3 (C) (3) (i) says:
(i) ownership in a mutual or common investment fund that holds securities is not a “financial interest” in such securities unless the judge participates in the management of the fund;
The cannons above are closely mirrored by 28 U.S. Code § 455 which provides:
(a) Any justice, judge, or magistrate judge of the United States shall disqualify himself in any proceeding in which his impartiality might reasonably be questioned.
(b) He shall also disqualify himself in the following circumstances:
(b) (4) He knows that he, individually or as a fiduciary, or his spouse or minor child residing in his household, has a financial interest in the subject matter in controversy or in a party to the proceeding, or any other interest that could be substantially affected by the outcome of the proceeding;
(d) For the purposes of this section the following words or phrases shall have the meaning indicated:
(d) (4) “financial interest” means ownership of a legal or equitable interest, however small, or a relationship as director, adviser, or other active participant in the affairs of a party, except that:
(i) Ownership in a mutual or common investment fund that holds securities is not a “financial interest” in such securities unless the judge participates in the management of the fund;
(ii) An office in an educational, religious, charitable, fraternal, or civic organization is not a “financial interest” in securities held by the organization;
Cannon 3 (C) (3) (i) and 28 U.S. Code § 455 (d) (4) seem to directly settle the question asked here.