Day-Lewis, who was accepting the Stanley Kubrick Award for Excellence in Film from Steven Spielberg, was addressing the audience when somebody placed an empty chair next to him on the stage, E! Online reported.
"I have to say, I'm so extremely grateful and glad that taking time out of his busy schedule, the recently re-elected president of this country was able to make it here tonight," Day-Lewis said, poking fun of Eastwood's infamous stunt.
"I know as an Englishman, it's absolutely none of my business, but I'm so very grateful it was you," he continued, pretending the empty chair was America's commander-in-chief.
"This is no satirical comment on him (Eastwood) or his politics or anything else," Day-Lewis said, "but I have to say that when I saw him talking to a chair to a room full of strangers, I thought, 'I've gotta try that. That's a challenge.'" Day-Lewis added, "I didn't pull it off quite as well as him, but anyhow, I've got some way to go."
And indeed, the actor, arguably one of the finest working today, loves a good challenge. Day-Lewis has his own presidential role in "Lincoln," directed by Spielberg, out in limited release on Friday.
[Related: Find showtimes and tickets for 'Lincoln']
Watch Daniel Day-Lewis and Steven Spielberg discuss 'Lincoln':