The SEAL team seized the unidentified target in a predawn firefight after approaching the beachfront house in the Somali town of Barawe by sea, the paper reported on its website
"The Barawe raid was planned a week and a half ago," the newspaper quoted an unnamed U.S. security official as saying.
"It was prompted by the Westgate attack," he added, referring to a militant assault on a Nairobi shopping mall two weeks ago in which at least 67 people were killed.
The Times quoted witnesses as saying that the firefight lasted more than an hour, with helicopters called in for air support.
The Times report quoted a spokesman for al Shabaab as saying that one of its fighters had been killed in an exchange of gunfire but that the group had beaten back the assault.
The U.S. officials said it was unclear whether the SEAL team's target was taken alive or killed.
The paper said a senior Somali government official confirmed the raid, saying, "The attack was carried out by the American forces and the Somali government was pre-informed about the attack."
Earlier, al Shabaab militants said British and Turkish special forces had raided the coastal town overnight, killing a rebel fighter, but that a British officer had also been killed and others wounded.
Britain's Defence Ministry said it not aware of any such British involvement. A Turkish Foreign Ministry official also denied any Turkish part in such an action.
A Somali intelligence official said the target of the raid at Barawe was a Chechen commander, who had been wounded and his guard killed. Police said a total of seven people were killed.