No, Instagram does not notify users when someone searches for their profile. When a person searches for someone on Instagram, the searched user will not receive any notification or alert about the search. This applies whether the search is done on the mobile app or the desktop site. The only way a user might know someone visited their profile is if the visitor interacts with their content, such as liking, commenting, saving posts, or viewing their Stories, since Story views notify the user.

Additionally, Instagram keeps search activity private and visible only to the person who performed the search. There is no feature allowing a user to see who has searched for them or viewed their profile unless this is through observable interactions (e.g., Story views).