Yes. Literally yes. Here are some examples.

• Men face oppression when taking their children out to give the mother a break(or if they're a single father) and people ask if the children know the father.(whilst the same cannot be said for women most of the time)
• A man can be sexually assaulted by his wife and almost no one will believe him due to the belief of "Men cannot be sexually assulted" and or "men cannot be raped"
• a man can be abused and will not be believed due to men being stronger than women and the belief that it is impossible for a man to be abused by a woman.
• Men are often seen as strong and "masculine" and show no emotion. But if a man isn't strong or "masculine" and shows his emotions. He is deemed to not be a man, and not masculine.
• Men are more often than not seen as likely pedos and are often creepy and or weird if a man is a teacher or a babysitter. Where as women are not seen that way as often as men are.
  

So yes. Men can face gender based oppression.