Molina appealed the ban and started Tuesday night, going 0-for-5 in the Cardinals' 5-3 win in 11 innings over the Milwaukee Brewers. He can continue to play until the process is complete. Lovullo will miss Tuesday night's game at San Francisco and was fined an undisclosed amount.
St. Louis manager Mike Matheny said he supported Molina's appeal.
"I don't blame him," Matheny said. "I probably would have done the same thing."
Molina had to be restrained after Lovullo, who came out to argue a called third strike against outfielder A.J. Pollock, gestured at him in the second inning of Arizona's 4-1 win.
Molina was restrained initially by plate umpire Tim Timmons and then by manager Mike Matheny after both benches cleared during the incident.
"[Lovullo] called me a m-----f----- twice," Molina said, according to KPNX-TV. "If you're going to call somebody that, you better be ready to fight."
Lovullo, who later acknowledged he "made a mistake with some of the wording that I chose," was ejected for leaving the dugout to argue balls and strikes. Timmons, in comments to a pool reporter, called Molina's contact with him "incidental" in explaining why the catcher wasn't ejected.
"We were hopeful that, especially with the report that we had from the umpire's comments, that it wouldn't carry over,'' Matheny said. "But it has, and now we'll have to deal with it."
Lovullo spoke earlier in the day with MLB executive Joe Torre, who explained the suspension to him.
"I support that, I agree with it, I made some mistakes,'' Lovullo said. "I'm passionate. I do things because of that passion that might be done the wrong way. And I said the wrong things, and I think that led to the whole thing. I have to serve the suspension, and I will do it.''
The Associated Press contributed to this report.