The centre-back pulled up with the issue in training last Friday.
Subsequently, Bruce was missing for Hull's 1-0 Premier League defeat to Southampton at the KC Stadium on Saturday.
"Alex got injured in training on Friday, one of the last kicks of the session," manager Steve Bruce told the club's official website.
"It's a hamstring but we don't think it's too serious. It's probably going to be two, three or four weeks."
The 30-year-old will definitely miss Hull's encounter at Burnley on Saturday before the Premier League takes a hiatus for the international break.
He could also be sidelined for the games with Tottenham, Manchester United and Everton when the top flight resumes.
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