Although nausea and vomiting are signs of concussion, without an seeing a actual hit that could have lead to a concussion, I would not say this is a concussion or concussion like symptoms. There are any number of things that cause vomiting. I have seen plenty of football players vomit during games and practice. Almost never is this related to a head injury.
I would handle this just like I would handle a bleeding player. Since vomit can contain infectious diseases just like blood, it is important to clean up the mess and make sure the player's uniform is clean.