"You have to have a shower and get rid of it because he's quite a nasty piece of work," he said of the title role in The Resistible Rise of Arturo Ui.
Originally based on Hitler, the Bertolt Brecht play has been reworked by Bruce Norris to include references to Trump.
"I don't think you could have avoided the connections," Norris told the BBC.
"In a play about totalitarianism you have to nod in that direction."
Set in Chicago in the 1930s, Arturo Ui tells of a gangster who uses bribery and intimidation to take control of the city's grocery market.
Norris's version sees Sir Lenny make a Hitler-style salute while using certain quotes that became associated with Trump during last year's US presidential election.
At one point Ui calls a female critic a "nasty woman", mirroring a remark Trump made during his final debate with rival Hillary Clinton.
At others he declares his intention to "make this country great again" and "build a wall", slogans that helped the tycoon turned politician take the White House last November.
"We started taking Trump quotes wholesale and shoehorning them into the play," said Norris, whose previous plays include the Tony- and Pultizer-winning Clybourne Park.
"They didn't require much adjustment. They were already chillingly close to what was already in the play."
"Bruce has definitely appropriated bits of Trump," said Sir Lenny after Tuesday's press night performance at London's Donmar Warehouse.
"But it's really a cautionary tale about any demagogue who uses their influence to ease their way into the upper echelons of society."
The role of Arturo Ui represents the comedian turned actor's latest foray into "serious" theatre, a career shift that began with him playing Othello in 2009.
"I still love comedy, but this is my career now," he explained. "This is me growing up and the journey that began with Othello continuing."
Early reviews of Simon Evans' production have praised Sir Lenny's performance, with the Evening Standard saying he brings "heavyweight authority" to his "smug bully" role.
"It's another casual tour de force from him that showcases his irresistible combination of talents," writes the Telegraph's Dominic Cavendish,
According to The Guardian, Sir Lenny "exudes massive authority" as he transforms "from a shambling klutz into a figure of authoritarian power".
Yet critic Michael Billington feels "there is something a touch glib about the [play's] frequent invocations of Donald Trump".
His reservations were echoed by The Arts Desk's Marianka Swain, who felt "the barrage of explicit references to 'The Donald' becomes a tad wearying".
The Resistible Rise of Arturo Ui runs at the Donmar Warehouse until 17 June.
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Sir Lenny Henry says he needs to wash off his latest stage role - a Chicago mobster modelled both on Hitler and Donald Trump - after each performance.