(CNN) -- A bullet thought to have been from a shootout between carjackers and municipal police in Ciudad Juarez, Mexico, struck a woman walking in neighboring El Paso, Texas, Tuesday morning, El Paso's mayor told CNN.
The still unidentified woman, 48, was shot in the lower leg; her injuries were not considered life-threatening.
El Paso Mayor John Cook said local police investigating the incident had not officially confirmed that the bullet came from Juarez, but they were "treating it as if it did," he said.
"It's still matter of speculation," he added.
"Early on, it became evident this may have been a stray bullet rather than a targeted shooting in downtown," local police said in a press release. "The El Paso Police Department continues its investigation and is working closely with its counterparts in Mexico."
If the bullet did in fact come from Mexico, this is "the first time a person has been hit" in the 3½ year since drug-fueled violence escalated in neighboring Juarez, Cook added.
In Juarez, a shootout between suspected carjackers and the municipal police happened around 11 a.m. (1 p.m. ET), about the same time the woman was shot, according to municipal police spokesman Adrian Sanchez.
He was unaware of any connection between that shooting and the incident in El Paso.
"We have an office that works with the U.S. and so far we have not received a report from them saying the two incidents were connected," he added.
El Paso police said that while they were responding to the shooting, the El Paso 911 center "received numerous calls advising of shots fired near the border in Juarez, Mexico."
Just about a mile separates downtown El Paso from Juarez.
"Under the right circumstances there is a possibility that a round fired from an AK-type weapon could travel that far, conceivably," Mike Brooks, HLN Law Enforcement analyst told CNN. "It depends on what kind of round it is and how heavy the round is."
"We're advising the citizens of El Paso that this is an isolated incident. We don't want people to start panicking," he said.
At least four schools in El Paso went on lockdown shortly after the woman was reported being shot.
"We were alerted by local police about concerns in the area," Estela Reyes, the press officer for the La Fe Preparatory School, told CNN. "We were in lockdown by 11:30 a.m. and lifted it about 30 minutes later. The kids were never in any imminent danger," she said.
Reyes said her school is about "seven or eight blocks" from downtown El Paso and she never heard gunfire from Juarez.
In June 2010, the El Paso City Hall was struck by several rounds, which local police believe the shots may have come from a shooting in Juarez.
About two months later, a similar incident occurred when a building at the University of Texas at El Paso was struck by a bullet. School officials believe that round also came from a shooting in Juarez.