WNBA's Brittney Griner & Fiancee -- Arrested for Assault ... Allegedly Attacked Each Other [Update]

9:06 AM PT -- According to the police report, obtained by TMZ Sports, Brittney told cops the two had been fighting for days and were having serious "relationship issues."

As for the specific incident, cops say there were several people at the home when Brit and Glory began to argue -- and the fight turned physical.

Cops say Brittney admitted to throwing a dog bowl at the wall -- and then the two began fighting.

Glory's sister eventually called police because people "couldn't get them pulled apart" and she didn't want anyone to get hurt.

When cops arrived, officers say Brittney had several cuts -- and a bite wound. Glory was bleeding from the lip.

The WNBA says it's actively investigating the incident.

WNBA superstar Brittney Griner -- and her WNBA star fiancee Glory Johnson -- were both arrested for allegedly attacking each other in Phoenix yesterday ... TMZ Sports has learned.

Law enforcement sources tell us cops were called to Griner's home around 4:30 PM on Wednesday -- after receiving a call about a domestic dispute between the two women.

When cops arrived, we're told officers observed "minor physical injuries" on both Brittney and Glory.

Both women were arrested and booked by the Maricopa County Sheriff's Office for assault and disorderly conduct. Griner and Johnson were released around 4 AM on Thursday.

Griner plays for the Phoenix Mercury.

The two got engaged last August and had been planning to get married next month in Phoenix. No word if the wedding is still on.

Glory and Brittney had been gushing about each other on social media in the days before the arrest.

In fact, Brit posted a pic of the two kissing on Tuesday with the caption: "EveryDay Every Second! I fall for you like I fell way back before I had the nerves to even approach you! My Queen My Rock My Universe!"