Lambert was led away by a police officer when he was dismissed following a scuffle on the touchline in the aftermath of a tackle by Jon Nolan on Max Aarons.
Ipswich went on to lose 3-0 to promotion-chasing Norwich and former Canaries boss Lambert opted not to contest the FA charge, meaning he will miss upcoming games against Wigan Athletic and Reading.
"Norwich City have been fined £25,000 and Ipswich Town have been fined £20,000 after accepting a charge for failing to ensure their players conducted themselves in an orderly fashion during both the 45th and 90th minutes, as well as their officials in the 45th minutes of their EFL Championship fixture on February 10," said an FA statement.
"In addition, Paul Lambert has been given a two-match touchline ban, effective immediately, and fined £3,000 after he also accepted an FA improper conduct charge concerning his behaviour in the 45th minute of the fixture."
Ipswich is bottom of the Championship table, nine points adrift of safety after winning one league game in two months, and Lambert is unsure what impact the ban could have on his struggling side.
"There was no point appealing because I wasn't going to win but I have had my say about what when on and I stand by every word," he told Ipswich's club website.
"I'll get on with it now. It's not ideal but I trust my staff to do what I ask them to do. There will be no problem there. Will it make a difference, not being on the touchline? I don't know. I can talk to the players before the game and after. They will know what is expected of them."