Savage used an expletive in his response to the fan, who criticized the GM in several e-mail exchanges.
"It happened after the game," Savage in an e-mail to The Associated Press. "There had been previous e-mails from him over the months and enough was enough. We have both apologized to each other since. The Browns' fans have overwhelmingly been supportive of me over the past 3-plus seasons and I appreciate that greatly."
Earlier, Browns coach Romeo Crennel said he spoke with Savage, who sent the e-mail moments after Cleveland's 29-27 win over the Bills in Orchard Park, N.Y.
"We all get frustrated at times," Crennel said. "Phil generally, like the rest of us, tries to be professional and hold it in. But sometimes some things slip out. It's unfortunate that it slipped out. Tough times, tough things happen. I'm sure that if we had it to do over again we'd do it a little bit differently."
Savage is not facing sanctions from the league.
"They have apologized to each other and put the matter behind them," NFL spokesman Greg Aiello said in an e-mail.
Savage's exchange with the fan was first reported on sports blog deadspin.com.
The fan, without revealing his name, appeared on WKNR radio in Cleveland on Thursday and said he had been badgering Savage throughout the game. During the fourth quarter Monday night, he said he sent Savage an e-mail calling him "the worst GM in the NFL." Savage replied about 40 minutes later with a short message that included an expletive.
"I'm highly embarrassed by it," the fan said. "I sent him two follow-ups. My second e-mail was an out and out apology to him."
Browns owner Randy Lerner did not immediately return an e-mail seeking comment.
The incident is just the latest episode in a tumultuous season for the Browns, who are a disappointing 4-6 after winning 10 games last season.
Last month, Savage was involved in a dispute with Pro Bowl tight end Kellen Winslow, who criticized the club for its handling of a three-day hospitalization for a staph infection. Winslow was initially suspended for one game for his comments, but the club later rescinded the penalty after learning that a team employee had sent a text message to Winslow telling him not to disclose he had staph.
The Browns have had at least six known cases of staph since 2005.
In addition, the Browns recently benched starting quarterback Derek Anderson in favor of backup Brady Quinn, who has gone 1-1 in two starts since getting the job. During his news conference on Thursday, Crennel revealed that Quinn broke his right index finger in the first half of Monday night's win over Buffalo.
Quinn, though, stayed in the game and is expected to play Sunday when the Browns host the Houston Texans.