Police say the man, who investigators have not identified, appears to arbitrarily choose his female victims.
Victims in the case gave similar descriptions of their alleged attacker: a Native American man, 5 feet 3 inches to 5 feet 6 inches tall, weighing approximately 165 pounds.
A blurry photo released by police shows a man in a dark T-shirt with orange and yellow type, blue jeans and a tan baseball cap.
The attacker may have victimized other women, said Farmington Det. Corp. Kenneth Raybon.
"We think he's been doing this since at least 2010, and he may not have stopped," Raybon said. "These are just the only incidents that have been reported."
The two incidents occured on March 29, 2010 and Nov. 8, 2012, Raybon said.
"We were able to tie the two instances together with evidence that recently came to light," he said.
Raybon would not say at which Walmart store the incidents occured. Farmington has two Walmart locations.
"We don't really want to single out Walmart because we think this may have happened in other retail stores," he said.
Police are seeking the man on suspicion of aggravated battery.
The Farmington Police Department is asking for the public's help in the case. The department's Detective Division can be reached at 505-599-1005. Those who wish to remain anonymous