Obama spoke alongside French President Francois Hollande a week after a large French business delegation travelled to Tehran to test opportunities that could be opened by the easing of Western sanctions.
"Businesses may be exploring -- are there some possibilities to get in sooner rather than later if and when there is an actual agreement to be had?" Obama said.
"But I can tell you that they do so at their own peril right now. Because we will come down on them like a ton of bricks."
Hollande, meanwhile, said that he did not control French corporations but had made clear sanctions on Iran would not be dismantled until a final deal on Iran's nuclear program had been reached.
"Sanctions will only be lifted if and when there is definite agreement," Hollande said.
"During this period of the interim agreement, they remain in force."
The 116-strong French delegation, with representatives from major companies like Total, Lafarge and Peugeot, was the largest of its kind from Europe since a landmark nuclear deal reached with the major powers in November gave Iran limited relief from crippling US and EU sanctions.