The Australian Federal Police won't take any action over a Queensland Labor election-day text message to voters claiming Medicare was under threat from the Coalition.

The Liberal Party filed a police complaint over the text message in the wake of the July 2 election result, but an AFP spokesman said on Tuesday no investigation or charges would proceed.

Voters reported receiving the text message urging them not to vote for the Coalition, which appeared to come from a sender under the name "Medicare".

"Mr Turnbull's plans to privatise Medicare will take us down the road of no return. Time is running out to Save Medicare," the message said.