Takeoff, whose off-stage name was Kirsnick Khari Ball, formed one-third of the Grammy Award-nominated trio Migos with uncle Quavo and cousin Offset from suburban Atlanta.
The 28-year-old rapper was killed early on Tuesday when gunfire erupted and also wounded another man and a woman, according to police Chief Troy Finner.
Most of the 40 people who attended the party at 810 Billiards & Bowling fled when the gunshots rang out, Finner said.
That left police asking people to come forward and give statements and videos to investigators on what they saw and heard, Mayor Sylvester Turner said.
At least two people discharged firearms, according to Finner. The two others who were struck by gunfire had non-life-threatening wounds and went to hospitals in private vehicles, he said.
Finner said Takeoff was "well respected" and there was "no reason to believe he was involved in anything criminal at the time".
Migos' record label, Quality Control, mourned Takeoff's death in a statement on Instragram.
"Senseless violence and a stray bullet has taken another life from this world and we are devastated," the statement said, though police have said nothing about the gunshot being a stray.
"Please respect his family and friends as we all continue to process this monumental loss."
Rap stars including Dave, Kid Cudi, Khalid, Sean Paul and Ja Rule also paid tribute.
The bowling alley is in a three-storey Houston retail complex. By late Tuesday afternoon, fans had created a memorial with roses, candles and a teddy bear on the first floor.
Migos first broke through with the massive hit Versace in 2013. They had four Top 10 hits on the Billboard Hot 100, though Takeoff was not on their No.1 hit Bad and Boujee.
They put out a trilogy of albums called Culture, Culture II and Culture III, with the first two hitting No.1 on the Billboard 200 album chart.
They also earned an ASCAP Vanguard Award in 2018 for their streaming success with multiplatinum songs such as Motorsport (featuring Cardi B and Nicki Minaj), Stir Fry, and Walk It Talk It.
The trio also played a fictional version of themselves on an episode of the hit TV show Atlanta, but the group was not currently together.
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