Goodyear police spokeswoman Lisa Kutis said the fight between the 24-year-old women was physical but no weapons were involved and neither required hospital care after sustaining minor injuries.
The players were booked into jail in Phoenix and later released. The Arizona Republic is reporting that the booking report indicates that the incident is being considered a domestic-violence offense.
According to police reports, Johnson's sister, Judy, called the police Wednesday afternoon while the couple was "in the living room throwing things at each other."
Griner told the police that she and Glory Johnson had been arguing frequently and on this occassion it was because Johnson felt Griner had "disrepected" her, according to a police report.
Johnson told the police she thought Griner was getting too so she gave her a push for some separation, and Griner responded by pushing her in the back of the head. The couple ended up fighting on the floor for 4-6 minutes, with the entire incident lasting about 20 minutes, according to the report.
"We couldn't get them pulled apart," Judy Johnson said, according to a police report.
Griner told officers: "It turned into a fight. Broke up. We kept arguing, mouthing back and forth, clashed again, separated us, clashed again, separated us, and here we are now."
The report also indicates that Griner nodded when asked if things got out of control.
Neither Griner nor Glory Johnson wanted prosecution.
Griner's injuries included what she described as a "tooth mark" on her hand, while Glory Johnson had lacerations on the right side of her lip, the police report said.
WNBA spokeswoman Dina Skokos said the league is working with both teams in gathering information about the alleged incident.
"The Mercury organization is aware of an alleged incident involving Brittney Griner," Mercury Executive Vice President and General Manager Jim Pitman said in a statement. "We are in the process of gathering additional information, and will have no further comment at this time."
Shock President Steve Swetoha said, "Of course our first concern is for Glory's well-being and health."
Griner was the league's defensive player of the year in 2014 and led the Mercury to the WNBA title the same season.