The 43-year-old Merson, who played for Wenger at Arsenal in the 1996-97 season, told French magazine So Foot that players were injected with a "yellowy product."
"I cannot take that comment seriously," Wenger told a news conference ahead of Sunday's Premier League home match with Aston Villa.
"I don't know how many players have played here in 15 years, 200 maybe, and some of them stayed with me for 10 years.
"Paul Merson stayed with me four months so I think it's better you ask people how we behave here medically who have played for five, six, seven, eight, nine years," added Wenger.
Merson played 425 times for Arsenal, scoring 99 goals, before Wenger sold him to Middlesbrough in 1997.
The former England player, who has a history of drug, alcohol and gambling addictions, also claimed Frenchman Wenger handed out "a dark tablet," which was high-powered caffeine, before one match.
But Wenger said: "I give them personally nothing. If they don't want to take anything, they take nothing.
"If you find one player that I asked to take something, bring him here in front of me. If we give them something it's multi-vitamins, magnesium or calcium or vitamin C like everybody else.
"Every year (we have) at least 20 doping controls. In 15 years we have not had one positive control. You think, really, I try to dope?," added Wenger.
"If you find one player who I asked to take an injection to play one game, no matter how big the game is, I resign tomorrow morning.
"It is absolutely ridiculous to put any suspicion on the way we treat the players... we respect the players' health."
