In granting preliminary approval, U.S. Magistrate Judge Henry Pitman in Manhattan said the payout appeared reasonable, citing an estimate by the interns' lawyers that it exceeded 60 percent of estimated unpaid wages.
"Given defendant's size and stature in the publishing world, I assume it could withstand greater judgment," Pitman wrote. "This fact, by itself, however, does not render the proposed settlement unfair."
The law firm Outten & Golden, which represents the interns, plans to seek legal fees of $650,000, or 11.1 percent of the settlement fund.
Pitman scheduled a June 22, 2015, fairness hearing to consider final approval of the settlement.
The lawsuit is one of many accusing media and entertainment companies of paying interns little or nothing for their work.
Comcast's NBCUniversal reached a $6.4 million settlement of a similar lawsuit in October. (Disclosure: Comcast is the owner of NBCUniversal, the parent company of CNBC and CNBC.com.)
Condé Nast canceled its internship program soon after it was sued in June 2013.
The case is Ballinger et al v. Advance Magazine Publishers Inc d/b/a Condé Nast Publications, U.S. District Court, Southern District of New York, No. 13-04036.