In the New York-based production, Julius Caesar is depicted as a blond-haired businessman in a blue suit.
The production company, Public Theater, said the character was a contemporary Caesar "bent on absolute power".
One of the sponsors, Delta Air Lines, said the producers had "crossed the line on the standards of good taste".
In the Shakespearean tragedy, which is staged in New York's Central Park, Caesar is assassinated in a lengthy scene in which he fights off his attackers before succumbing to multiple stab wounds.
The lead character's wife in the play, Calpurnia, is depicted wearing designer outfits and speaking with an apparent Slavic accent.
In announcing the production earlier this year, Public Theater described its portrayal of the Roman leader as "magnetic, populist and irreverent".
On its website, the company states that the play is about "how fragile democracy is," adding that it highlights how the "institutions that we have grown up with can be swept away in no time at all".
Delta said on Monday that the "graphic staging of Julius Caesar" at the Free Shakespeare in the Park event "does not reflect" the airline's values.
President Trump's son, Donald Junior, criticised the production, asking whether boundaries had been crossed in what he described as art becoming political speech.
"I wonder how much of this 'art' is funded by taxpayers?" he tweeted, adding: "Serious question, when does 'art' become political speech & does that change things?"
The play opened with previews on 23 May and the production is due to run until 18 June.
Delta and the other sponsor to withdraw, Bank of America, have both supported the Shakespeare season in Central Park for several years.
In a 2012 production of Julius Caesar by New York-based The Acting Company, the Roman leader was modelled on then-President Barack Obama.