Archer, 19, was placing the ball for a goal kick when the supporter came onto the pitch and leapt towards him.
The keeper, on loan from Tottenham Hotspur, was unharmed and the fan was quickly led away from the pitch by stewards.
"Some people give the rest of the Gillingham fans a bad name," Wycombe boss Gareth Ainsworth told Sky Sports News.
"I don't want to comment too much, but everyone is okay in there."
The match ended 1-0 to Wycombe.