Footage was shared on social media alongside comments claiming he smashed the device as he left the pitch after his side's 1-0 loss at Everton.
Ronaldo, 37, later apologised on social media.
Merseyside Police said they were investigating "reports of an alleged assault" at Goodison Park on Saturday.
A spokesperson said they were liaising with both Manchester United and Everton.
"As players were leaving the pitch at 2.30pm, it was reported that a boy was assaulted by one of the away team as they left the pitch," they added.