United ran out 2-0 winners at Elland Road but the match was soured by supporters trading chants about the Munich air disaster, which killed eight United players in 1958, and the death of two Leeds fans in Istanbul in 2000.
"The Premier League condemns the chanting heard during today's match between Leeds United and Manchester United," the league said in a statement.
"The League is treating the issue of tragedy chanting as a priority and as a matter of urgency."
There have previously been calls from Liverpool fans for the Premier League to take action on chanting about the 1989 Hillsborough disaster.
In a joint statement after the match, Leeds and Manchester United said:
"Both clubs strongly condemn chanting from both sets of fans regarding historic tragedies at today's game.
"Such behaviour is completely unacceptable and we will continue to work together with our respective fan groups and the Premier League and other authorities on eradicating it from football."
