No, there is a null result
Detect Magic (PHB, 231) works as follows:
For the duration, you sense the presence of magic within 30 feet of you. If you sense magic in this way, you can use your action to see a faint aura around any visible creature or object in the area that bears magic, and you learn its school of magic, if any.
The spell can penetrate most barriers, but it is blocked by 1 foot of stone, 1 inch of common metal, a thin sheet of lead, or 3 feet of wood or dirt.
So what we have is a character casting detect magic withing range of the wizard. Magic in range should be sensed, after which the character could use an action to see a faint aura about the wizard and learn the school of magic.
But then the rules around the antimagic field (PHB, 213) come into play.
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.
Areas of Magic. The area of another spell or magical effect, such as fireball, can't extend into the sphere. If the sphere overlaps an area of magic, the part of the area that is covered by the sphere is suppressed. For example, the flames created by a wall of fire are suppressed within the sphere, creating a gap in the wall if the overlap is large enough
Spells. Any active spell or other magical effect on a creature or an object in the sphere is suppressed while the creature or object is in it.
Dispel Magic. Spells and magical effects such as dispel magic have no effect on the sphere. Likewise, the spheres created by different antimagic field spells don't nullify each other.
Okay, so we've got a few things in here.
Detect Magic can inherently be stopped by certain barriers. An anti-magic field is a barrier of sorts. While it isn't explicitly mentioned in detect magic, there is an existing rule that the detect magic can be stopped. We can now look at the language of antimagic field to see if it would qualify.
Antimagic field clearly suppresses any magic (except those created by an artifact or a deity.) Detect magic is not created by an artifact or deity so should be suppressed as a whole. It can't protrude into it, and therefore wouldn't be detected. There is nothing to detect. The additional stipulations in areas of magic and **spells* also are clear in that no magic passes the barrier.
The rules in antimagic field about dispel magic also imply that interactions between the field and other spells have no effect. Just like how dispel magic can't interact with the field, neither can detect magic.
Narratively, the character casts detect magic, but they get a null result from the field. If the character knows that they have magic items on them and they don't get a response, then they'll know something is up. But otherwise, the reading from detect magic comes up with no magic (at least from the antimagic field.)