RCMP say the caller told the woman on Saturday that she was trying to reach her grandmother, Katherine Pierce, to say she had run into a tree while riding with her sister about six or seven kilometres from Carrot River.
The caller said her name was Cassandra, but there's no last name.
She told the woman she was disoriented and couldn't remember her grandmother's phone number.
The number she called from was blocked and police say they haven't been able to trace it.
Staff Sgt. Chad McLeod says investigators have tried to find the grandmother but haven't had any success.
"They've tried to find 'Katherine Pierce' in the Carrot River or Nipawin areas and there's nobody, and that just adds to the mystery," McLeod said.
He said the information was also clouded by the fact that it was being relayed to police second-hand from the woman who got the wrong-number call.
"The lady did the best she could but she was probably caught off guard at the time," McLeod said.
Police say they are concerned about the well-being of the two people.
In 2010, Kerri Canepotatoe, 18, died after walking for help when she and three others got stuck on a logging road in Saskatchewan and a civilian RCMP dispatcher got distracted and forgot to send a tow truck.
Her cellphone call to an RCMP call centre died, and while she was able to give partial directions about her location, a robbery call came in afterward and the dispatcher never forwarded the information for followup.
McLeod said the call about the snowmobilers could be a hoax, but police don't know that, and must continue to search for them until they determine otherwise.
"We have to keep going until we rule out other options," McLeod said.
McLeod said there isn't a lot of snow around Carrot River at the moment, which means there aren't a lot of trails the snowmobilers may be on.
He said police are hopeful that the caller, if she is safe, will see media reports about the search and call RCMP to let them know.
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