Thunder All-Star Russell Westbrook was hurt when Beverley tried for a steal in the second quarter of Game 2 of the teams' Western Conference first-round series and ran into his knee. Westbrook had knee surgery on Saturday and is out for the season.
The tweets were deleted as of Saturday night, but the Houston Chronicle says a tweet from the handle @MitchellBrwn said: "Patrick Beverly (sic), I'm coming to kill you."
He later sent another one with Beverley's Twitter name, saying: "@pavbev21 I'm coming to kill you."
He later apologized in one tweet and then said he was hacked in another post.
Oklahoma City police captain Dexter Nelson tells The Associated Press that their department is working with the Houston police and the NBA to investigate the threats.
The Thunder says in a statement that they "do not condone his comments. He works game nights on a voluntary basis and the matter will be handled internally."
Game 3 was Saturday night in Houston. Security was increased for the game, but it was done because of the Boston Marathon bombings.