Police responded to a 911 call reporting an assault at 6:45 a.m. and arrested Porter, 23, after an investigation. Both charges are felonies.
The incident involved Porter's girlfriend, a former WNBA player, sources told ABC News.
"Upon arrival officers were informed that a 26-year-old female sustained a laceration to the right side of her face and was complaining about pain to her neck," the spokesperson said. "A preliminary investigation on scene determined that a known individual struck her multiple times upon her body and placed his hands around the neck."
The woman was transported to the hospital for evaluation, the police spokesperson said.
"We are in the process of gathering information surrounding the matter involving Kevin Porter Jr.," the Rockets said in a statement. "We have no further comment at this time."
The NBA also acknowledged Porter's arrest, saying in a statement through spokesman Mike Bass: "The league office is in contact with the Houston Rockets and in the process of gathering more information."
While the NBA is conducting its own investigation, the Rockets aren't allowed to administer any immediate punishment on Porter, including a suspension.
Under the terms of the league's domestic violence policy, commissioner Adam Silver has the power to place Porter on administrative leave with pay for "a reasonable period of time." Based on the findings of the case, the commissioner can fine, suspend, dismiss or disqualify from any further association with the league and its teams a player who violates the domestic violence policy.
Porter signed a four-year contract extension worth as much as $82.5 million last season. However, it is only partially guaranteed due to Porter's history of off-court issues. If the Rockers were to eventually waive Porter based on the results of this investigation or a criminal conviction, the franchise would be responsible for only the $16.9 million of guaranteed money left on his contract.
Porter was the No. 30 pick in the 2019 draft after spending one season at USC, where he was suspended because of conduct issues. He played his rookie season for the Cleveland Cavaliers but did not join the team the next season due to personal reasons. He was traded to the Rockets for a top-55-protected second-round pick in January 2021 in the wake of a shouting match with Cleveland team officials.
ESPN's Adrian Wojnarowski and Bobby Marks contributed to this report.