The 19-year-old goalkeeper - on loan from Tottenham - was placing the ball prior to taking a goal kick when the supporter entered the field and leapt towards him at the Priestfield Stadium.
The fan was quickly apprehended by a steward and led away.
Kent Police said on Tuesday morning: "A 17-year-old was arrested on suspicion of assault and is currently in custody following an incident in the 93rd minute of the Gillingham v Wycombe match last night."
Wycombe boss Gareth Ainsworth told Sky Sports 1: "Some people give the rest of the Gillingham fans a bad name.
"I don't want to comment too much, but everyone is okay in there."
Gills boss Martin Allen was quick to condemn the incident. He said: "As a football club we can't condone (what happened). None of us are happy with that."
The incident comes in the same season that Sheffield Wednesday goalkeeper Chris Kirkland was attacked by a Leeds United fan.
Aaron Cawley, 21, from Cheltenham, was jailed for 16 weeks after he pleaded guilty to assault and invading the pitch during October 19's clash at Hillsborough.
Cawley ran on to the pitch during the celebrations following Leeds' equaliser and shoved Kirkland in the face.
The incident, like Monday night's at Gillingham, was captured live by Sky Sports cameras.