Team-mate Abdoulaye Faye whacked Smith in the face by accident in the 2-1 defeat at Chelsea.
The England star, 27, received treatment and played on for a short time but was subbed with 20 minutes left.
He flew back from London to Newcastle with his team but felt unwell on the plane.
Smith, a £6million buy from Manchester United in the summer, went to hospital on the advice of the club doctor and was kept in overnight.
Checks were made on his condition before he got the all-clear to leave yesterday.
Smith's agent Alex Black said: "Alan couldn't remember much after getting hurt and the club felt he should have a proper examination.
"He was allowed out on Sunday morning when he was feeling a lot better."
Smith hopes to be available to face Manchester City at St James' Park on Wednesday.