Baseball disciplinarian Bob Watson told The Associated Press on Tuesday night that the league is looking into the matter, calling it "serious."
A handful of Rockies players exchanged words with the umpiring crew during and after the game.
Second base umpire Bill Miller called Yorvit Torrealba a derogatory name while the catcher was a baserunner late in the game, the Denver Post reported. That escalated tensions on a night when both teams complained about the ball-and-strike calls of umpire Angel Campos.
After the game, which the Rockies won on Ryan Spilborghs' grand slam, Torrealba exchanged words with Miller as the crew that included Derryl Cousins and Jim Joyce tried to work their way through the Rockies' celebratory scrum and exit the field through a fence behind home plate, the paper reported.
On Tuesday, Torrealba said he wasn't worried about being fined or suspended.
"I didn't do anything wrong, why should I worry?" Torrealba said after the Rockies' 5-4 extra-inning win over Los Angeles on Tuesday night. "I won't take anything from anybody. If you offend me, I'll offend you. If you respect me, I'll respect you."
Torrealba explained to the paper that he bit his tongue during the game because he couldn't risk getting thrown out, but afterward let loose on Miller for what he considered the umpire's inappropriate remarks.
The umpires filed an incident report but Watson said he needed to speak with more people about what happened before deciding on any disciplinary measures, which could come as early as Wednesday.
"We are investigating," Watson told the AP. "This is a serious matter and we will take a serious look at it. We're looking at both players and umpires."
Miller was the first base umpire in Milwaukee on Tuesday night and he declined comment through a Brewers spokesman.
If Torrealba is suspended, the Rockies, who lead the NL wild-card race and are two games behind the Dodgers in the NL West, will have to make a roster move because they wouldn't have anybody to back up catcher Chris Iannetta.
Other Rockies who face possible punishment for jawing with the umpires include shortstop Troy Tulowitzki -- who also was chastised by the umpires for high-fiving Spilborghs before he had crossed home plate after his walkoff grand slam -- and closer Huston Street.
Torrealba told the Post that Miller insulted him while telling him he was out of line to show up Campos through his body language on calls he didn't feel were going the Rockies' way.
As Miller and Torrealba argued, Street hollered at Joyce, who was umpiring first base, telling him Miller needed to stop. Joyce came over to the rail of the Rockies' dugout and exchanged words with both Street and pitching coach Bob Apodaca.
Rockies manager Jim Tracy said he didn't believe anybody would be disciplined over the matter.