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The video was never posted to Leonard's verified Twitch channel, but the individual in the video appears to be the same person shown in other videos posted to Leonard's channel on Monday.
Leonard says he's "committed to properly seeking out" those who can educate him on "this type of hate and how we can fight it."
"I acknowledge and own my mistake and there's no running from something like this that is so hurtful to someone else," Leonard said.
Leonard did not allude to the sexist part of his remark in the apology.
NBA spokesman Mike Bass told CNN in an email the league "just became aware of the video and are in the process of gathering more information."
"The NBA unequivocally condemns all forms of hate speech," Bass' email said.
The Heat released a statement saying the organization "vehemently condemns the use of any form of hate speech."
"The words used by Meyers Leonard were wrong and we will not tolerate hateful language from anyone associated with our franchise," the team's statement read. "Meyers Leonard will be away from the team indefinitely. The Miami HEAT will cooperate with the NBA while it conducts its investigation."
CNN Sports has reached out to Leonard's agent, but has not heard back.
"ASTRO is committed to creating an inclusive gaming environment and one that combats racism and other forms of discrimination, retaliation and harassment. For that reason, we are ending our relationship with Meyers Leonard, effective immediately," ASTRO Gaming's statement read.
Leonard has played in three games for the Heat this season. He underwent left shoulder stabilization surgery on February 2 and is expected to miss the rest of the season.