During the White House correspondents' annual dinner Mr Obama showed a picture of a White House with girls in bikinis sipping cocktails in a hot tub.
The president also made fun of rumours that he was not born in the US.
Mr Trump, a potential Republican presidential candidate, had recently revived the conspiracy theory.
Mr Obama said that after he released his long-form birth certificate this week in order to settle the issue, Mr Trump could now turn his attention to more serious matters such as, "Did we fake the Moon landing?"
During the dinner comedian Seth Meyers also teased Mr Trump, who sat stony-faced through the barrage.
"Donald Trump often talks about running as a Republican, which is surprising," said Mr Meyers. "I just assumed he was running as a joke."
US President Barack Obama has sent up Donald Trump's presidential ambitions, joking that the real-estate mogul would turn the White House into a casino.