Kerrynne Liddle issued a statement about the blunder on Friday evening.
"To the family who have lost a loved one, I offer my sincere apologies for what you have been through and for any confusion to the broader community," Senator Liddle said.
"The concerns raised were based on information available at the time."
Senator Liddle, a South Australian member of the Liberal Party, initially claimed the woman died because emergency calls to triple zero did not get through.
A police investigation found those suggestions were incorrect.
The woman was found unresponsive at 10am on Wednesday.
Her partner called a neighbour, who had medical experience, via a Telstra phone and the call was connected.
The neighbour, who also had a Telstra phone, later called triple zero.
"Both of those calls went through without any difficulty," SA Police Commissioner Grant Stevens told reporters.
"The woman was then conveyed to a local hospital where she later passed away."
Incorrect suggestions the death was related to the Telstra outage put unnecessary strain on the family, Mr Stevens said.
"This is a tragedy where a family has lost a loved one and in the ordinary course of events, they would not have had such significant involvement with the South Australia Police and this particular person's passing would not have been the subject of such significant scrutiny," he said.
Federal Communications Minister Anika Wells said it was a relief there had been no deaths linked to the Telstra outage, but criticised Senator Liddle for making the claims.
"There is no causative link between the outage and this tragic death whatsoever," Ms Wells told reporters in Canberra
"The opposition have a lot to account for in their conduct out of this week."
Opposition Leader Angus Taylor has been criticised for raising, without evidence, the prospect of China being responsible for the Telstra outage.
His communications spokeswoman Sarah Henderson has also been scolded for making unnecessary calls during the Telstra outage to triple zero, which carries a criminal penalty.