Antimagic Field states the following:
Spells and other magical effects, except those created by an artifact or a deity, are suppressed in the sphere and can't protrude into it.
So in order to answer your question, we have to determine whether or not Petrifying Gaze constitutes a magical ability/attack,
Unfortunately, the source books for Fifth Edition do not provide an explicit definition for what exactly constitutes a magical ability. However, there exists an overall consensus summarized here based off the Sage Advice Compendium. Jeremy Crawford's original tweet neatly sumarizes the ruling as such:
A monster's attack is magical if its text says so.
The Medusa's Petrifying Gaze makes no mention of the attack being magical, so the effect would not be dispelled or prevented by Antimagic Field.
Overall, there is ample precedent to support this interpretation. This answer establishes that a Dragon's breath weapon is not considered magical based on similar logic, so I would say that the strongest interpretation is that the Medusa's Petrifying Gaze is not affected by Antimagic Field.
However, there's more information to consider.
If you're feeling creative... sort of yes.
According to the Monster Manual, Medusas are created under the following conditions:
Men and women who seek eternal youth, beauty, and adoration pray to malicious gods, beg dragons for ancient magic, [...] seek out powerful archmages, [or] make sacrifices to demon lords or archdevils, offering all in exchange for this gift, oblivious to the curse that accompanies it.
A curse could easily constitute a "magical effect" as defined in the text for Antimagic Field.
So, as long as the curse was not bestowed by a god/deity, an interesting interpretation would be that the Medusa is temporarily freed of its curse, such that it would be unable to use its normal abilities.
Opinion: as a DM, I would say yes.
As the text for the Medusa's ability is vague in this context, I personally would rule in favor of the Antimagic Field suppressing the ability. The abilities of a CR6 creature like the Medusa should be trumped by a Level 8 spell like Antimagic Field, and both thematically and intuitively it makes sense that Antimagic Field would work in this way.
Additionally, I think the player's satisfaction at overcoming the Medusa in such a way is enough that I would rule in their favor regardless of the interpretation. Ruling against the player for situations like this break "the rule of fun" and can sting strongly of killing something interesting simply for the sake of a technicality.