Authorities in Medina, Minn., released the details one day after Cunningham was jailed for another alleged incident with the woman he had been living with for the previous eight months. Cunningham had already been charged with felony domestic assault for allegedly choking the woman last week.
Police said they received a call from the woman in the early-morning hours Sunday saying that Cunningham had violated a protection order by contacting her.
"When the officer arrived and reviewed the messages, they were direct and rose to a terroristic level," the police statement read.
Cunningham surrendered Sunday and turned over his cellphone and computer as part of the investigation. The Associated Press left a message with Cunningham's attorney seeking comment.
Cunningham remained in custody after his second arrest but has not been charged. He was scheduled for an initial court appearance Monday afternoon related to his assault charges.
The Timberwolves said Sunday they were gathering information about the latest arrest.
"The situation with Dante Cunningham is very fluid, and we continue to monitor all available information," the team said. "We reiterate that the Minnesota Timberwolves do not condone the behavior described in the accusations. We continue to wait for the legal process to run its course and will have further comment when appropriate."
Cunningham played for the Timberwolves in Orlando on Saturday night, starting against the Magic for the injured Kevin Love and getting 12 points and six rebounds in 34 minutes. The NBA's collective bargaining agreement requires the league to allow players to work while the legal process plays out.
In his fifth year in the league, Cunningham is averaging 6.1 points and 4.1 rebounds. He is set to become a free agent on July 1, after completing the final year of a contract that pays him $2.1 million this season.
Dante Cunningham Charged With Assault
ESPN legal analyst Lester Munson breaks down the latest on Timberwolves forward Dante Cunningham, who has been charged with one felony count of domestic assault by strangulation after allegedly choking his girlfriend.