He could face further punishment from the NFL.
"It's a closed case," coach Bill Belichick said Wednesday. "I really don't think it's appropriate to talk about details and circumstances."
Belichick said his decision was made independently of any punishment the NFL might hand down.
League spokesman Greg Aiello said the NFL will determine whether Law violated its substance abuse policy.
A first-round draft pick for the Patriots in 1995, Law signed a seven-year, $50-million contract extension last summer.
He has 22 career interceptions, ninth on the Patriots' career list.
Law and wide receivers Terry Glenn and Troy Brown were given permission to stay in Buffalo after last Sunday's game against the Bills so they could wait out a snowstorm.
The players went to a strip club across the border, and when Law attempted to cross the border at 5:30 a.m. Monday to catch his return flight, U.S. Customs inspectors searched the car and found some pills later identified as MDMA, commonly known as ecstasy.
Because the amount of drugs was small, Law paid a $700 fine and was allowed to continue on his way.
But he missed his flight and was late for a team meeting, as were Glenn and Brown, who waited for him at the airport.
Belichick wouldn't say if Glenn and Brown would be disciplined.
Neither Glenn, Brown nor Law were in the locker-room on Wednesday during the period it was open to reporters.
In offering an apology Tuesday, Law said the drugs were found in a suitcase that belonged to a cousin who stayed at his home.
"I had no idea that it was in the bag," he said, offering to take a drug test to prove he is clean.
"I know this sounds stupid and maybe a little bit unbelievable, but that's the truth, the honest-to-God truth."
Asked whether he believed his player's explanation, Belichick said, "It's not about that."
He repeatedly refused to elaborate on the suspension other than to say he thought it was a matter best handled within the team.
"Every season, there are distractions that you deal with," quarterback Drew Bledsoe said. "And this is no different."
In 1997, Bledsoe and guard Max Lane were sued by a woman who claimed she was injured when they dove off the stage during an Everclear concert at a Boston nightclub.
Three days after the incident, the Patriots lost to Tampa Bay.
In 1998, punt returner Dave Meggett was arrested and charged with sexually assaulting a call girl at a Toronto hotel room during the off-season.
Last September, tight end Rod Rutledge crashed into two trucks when he lost control of his car during what police said was a race with tight end Ben Coates.
On Thanksgiving Day, Glenn was charged with reckless driving after police caught him going 65 to 75 m.p.h. in a 30 m.p.h. zone on his way to practice.
A month later, coach Pete Carroll suspended Glenn for the season's final game for failing to check in with the team and missing meetings while he had the flu.
"This job changes a bit every week," said Belichick, who replaced Carroll during the off-season.
"There are different challenges to deal with every week."
Regardless of what happens against Miami on Sunday, the Patriots (5-10) have been worse in each of four consecutive seasons since making it to the 1996 Super Bowl.
But Belichick said he doesn't think a failing team is more likely to have disciplinary breakdowns.
New England's Super Bowl years, 1986 and '96, have been among the most disruptive.
Wide receiver Irving Fryar missed the '86 AFC championship game after he was cut with a knife in a mysterious incident involving his wife; in '96, news that coach Bill Parcells was planning to defect to the Jets broke during Super Bowl week.
"When a team's losing, obviously everything that's negative is really magnified," Miami coach Dave Wannstedt said. "I don't think these incidents happen any more when a team's losing.
"I just think the focus is on them a lot more."
By Jimmy Golen