Capt. John Babin of the Lafayette Metro Narcotics Task Force confirmed the summons on Tuesday.
Faulk, a Louisiana native and former LSU star, was on his way to a suite in the Lafayette Cajundome to watch a performance by rapper Lil Wayne, when a routine search by a sheriff's deputy turned up four marijuana cigarettes, Babin said.
Everyone heading to the suites was searched, Babin said.
Faulk was not arrested or required to post bond.
"He was cited for simple possession, which is a misdemeanor," Babin said. "It's based on an amount possessed for personal use."
Faulk will be sent a letter notifying him of the court date when it is set.
"There was no trouble, Kevin was very cooperative," Babin said.
"We are aware of the report, but I don't have any additional comment at this time," Patriots spokesman Stacey James said.
Faulk, a captain last season for the first time in his nine years with the Patriots, had 47 catches for 383 yards and one touchdown, the winner in a come-from-behind 24-20 victory over Indianapolis on Nov. 4. He's the team's all-time leader in receptions by a running back with 323.
Faulk also had 62 rushes for 265 yards in the Patriots 18-1 season, which ended with a 17-14 loss in the Super Bowl to the
New York Giants.
He made big plays in two of the Patriots' Super Bowl wins. His 2-point conversion reception gave the Patriots a 29-22 lead in their 32-29 Super Bowl win over Carolina in the 2003 season. The next year, he made a 12-yard catch to Philadelphia's 2-yard line that set up the Patriots' third touchdown in a 24-21 Super Bowl win.
The 5-foot-8 Faulk ended his college career as the leading rusher in LSU history with 4,557 yards.
On Feb. 5, one of Faulk's teammates, defensive back Willie Andrews, pleaded not guilty to a marijuana possession charge in Lawrence, Mass., after police said they found him with a half-pound of marijuana. Andrews, who just completed his second year with the team, is free on his own recognizance. A pretrial conference in his case is set for March 18.