The striker, currently on a season-long loan from Sunderland, clashed with Gareth Barry against Everton on Saturday before being stretchered from the field of play
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The club tweeted: "Danny Graham is set to be sidelined for around three weeks with the injury he suffered in Saturday’s game at Everton.
"Although scans have revealed the striker escaped serious injury following a first-half challenge by Gareth Barry, severe bone bruising around the knee will keep the on-loan Sunderland man out of action until next month."
Graham is yet to score in seven Premier League appearances for Steve Bruce's men.