The two 24-year-olds were each arrested Wednesday on counts of assault by recklessly causing physical injuries and disorderly conduct for fighting. They were booked into the Maricopa County Jail in downtown Phoenix and later released.
"The last few months have been an extremely stressful time for Brittney and Glory. They will continue to work through these hardships together and ask that the media respect their privacy as they handle this family matter," Griner's attorney, David Michael Cantor, said in a statement released Thursday. "Glory and Brittney sincerely apologize for the distraction this has caused their families, respective teams, the WNBA, sponsors and fans."
The agent for Johnson did not immediately respond to a request for comment Thursday.
Griner told police that she and Johnson had been arguing every day and got into each other's faces Wednesday afternoon in the home they had bought two days earlier after Johnson said Griner "disrespected" her, according to a police report.
Johnson told police Griner had gotten too close, so she pushed her back to get some separation and began talking to her sister, Judy Johnson, when she was pushed in the back of the head by Griner. Glory Johnson turned around and the physical altercation began, with both fighting on the floor for 4 to 6 minutes. The entire episode lasted about 20 minutes, according to the report.
Griner had a laceration on her right wrist and a tooth mark on the middle finger of her right hand after it ended up in Glory Johnson's mouth, according to the police report.
Johnson, who plays for the Tulsa Shock, had a cut on her lip and Julio Trejo, a friend of Griner's, had a cut on his neck after trying to break up the fight. All three declined medical attention.
Griner also said she broke a dog bowl after throwing it against a wall during the argument.
Griner told police the fight was caused be weeks of stress, including buying a house, planning a wedding and their relationship. The pair announced their engagement late last summer and expected to get married next month.
The WNBA and the teams said in statements that they were looking into the situation and did not comment further.
"Of course our first concern is for Glory's well-being and health," Shock President Steve Swetoha said.
WNBA spokeswoman Dina Skokos said the league was working with both teams to get more information.
Griner helped the Phoenix Mercury win their third WNBA championship last September. She led the league with a record 129 blocks and was the WNBA Defensive Player of the Year. She also helped the U.S. win a gold medal last fall at the world championships.
Griner is a two-time AP college basketball player of the year and led Baylor to a 40-0 season and the 2012 NCAA title. She was the No. 1 pick by the Mercury in the 2013 draft.
AP Basketball Writer Doug Feinberg and AP Writer Paul Davenport contributed to this report.