The Conservative politician was visiting the Leeds hospital after the Yorkshire Evening Post revealed that four-year-old Jack Williment-Barr had been forced to sleep on the floor after a trip to the A&E department.
Mr Hancock met the hospital's chief executive and said he was said he was "horrified" by the photograph.
Outside he was heckled by protesters who "shame on you" and "you are not welcome in this hospital, you are not welcome in this country".
Rumours that Mr Hancock's aide was "punched" began to circulate on social media after he had left the hospital.
In a now deleted tweet, BBC political editor Laura Kunsberg said: "So Matt Hancock was despatched to Leeds Hospital, to try to sort out mess, hearing Labour activists scrambled to go + protest, and it turned nasty when they arrived - one of them punched Hancock's adviser."
She has since apologised after seeing a video of the alleged incident, which she shared on Twitter.
She said: "Have video from Hancock leaving Leeds General just come through so you can see for yourself - doesn’t look like punch thrown, rather, one of Tory team walks into protestor’s arm, pretty grim encounter."
Later, she added: "Happy to apologise for earlier confusion about the punch that wasn’t a punch outside Leeds General - 2 sources suggested it had happened but clear from video that was wrong."
A West Yorkshire Police spokesperson said that the force is currently "unaware" of any reports in relation to the incident.
The spokesperson said: "We are aware of information circulating on social media in relation to an alleged incident involving election campaigners at Leeds General Infirmary this afternoon.
"We are currently unaware of any reports to West Yorkshire Police of this nature but are seeking to verify."