Götblad suffered an accident in her home that seriously injured her knee and left her unable to reach the telephone.
Instead, she used an emergency call button with a direct link to Säpo in an effort to get help – but no one came.
The agency is now investigating the incident, the Aftonbladet newspaper reports.
“We view what happened very seriously,” Säpo spokesperson Patrik Peter told the newspaper.
The accident took place toward the end of last week when Götblad fell and injured herself in her apartment in Stockholm.
When no one from Säpo showed up, she was forced to crawl out onto the street where she received help from a passer-by.
She was eventually taken to hospital in an ambulance to undergo an operation for the injury.
Säpo has now launched an internal investigation into why the alarm didn’t function properly.
“It remains unclear as to whether it was a technical malfunction or an error in how the call was handled,” Peter told the newspaper.