The message was to ask Lamara Bell if she knew the whereabouts of a cousin who had gone missing.
A senior Police Scotland officer has visited the family to apologise.
Ms Bell and John Yuill were left in their crashed car at the side of the M9 when police failed to respond to reports of the vehicle off the road.
Forth Valley Divisional Commander John Hawkins said: "Once again I want to offer Police Scotland's condolences to the family.
"I am deeply disappointed that we have shown such a lack of awareness given all the briefings put in place within the area and the media coverage reflecting the level of shock felt across the country.
"We clearly regret having caused any further upset to them.
"I have given all the details to the family of why the call was made and given my, and the Chief Constable's sincere apologies on behalf of the force."
Mr Yuill was found dead and Ms Bell critically injured on Wednesday 8 July in a car that had crashed off the motorway near Stirling.
It subsequently emerged that the crash had been reported to police by a member of the public the previous Sunday.
Officers only attended the scene after receiving a second call from a different person.
Ms Bell later died in hospital from injuries that included broken bones and kidney damage caused by dehydration.
Sir Stephen House, the Chief Constable of Police Scotland, has admitted that his force had "got things badly wrong" over its handling of the tragedy.
A review into the way the police handle calls in their control centres is to be carried out, examining how control centre systems and staff manage, answer and prioritise calls.
The Scottish Conservatives accused Police Scotland of being in "chaos".
Justice spokeswoman Margaret Mitchell said: "Calls are not being dealt with correctly and simple information - which should be at people's fingertips - is clearly not being passed on at a local level."
Scottish Labour's justice secretary Hugh Henry said: "This is a shambles and unfortunately it damages the credibility of Police Scotland even further.
"Someone, either in government or the police, must take responsibility for all this."
Police have apologised to the family of a woman left dying in a car for several days after an officer left her a voicemail 10 days after her death.