Bags containing IV tubes and “pooled blood” were found in the street by a “shocked” passer-by.
Toby Robson found several biohazard bags to his “horror and disgust” in Prospect Place, Swindon, on Saturday.
The parish councillor said that on closer inspection, he was “appalled” to find they contained clinical waste.
The council removed it but another bag has since appeared in the same place. A spokesman said the incidents were “disturbing”.
It is not known who the waste belongs to.
They require disposal by incineration.
Mr Robson said: “I was walking with my kids on our way home on Prospect Place when I saw the biohazard signs on the bags and I did a classic double take.
“My partner is a nurse and I asked whether waste like this should be out on the street. She was as shocked as I was.
“The fact that these bags were within yards of several restaurants as well beggars belief. My partner took the kids home and I stayed to organise a removal.”
Mr Robson, who has called for an investigation, said Swindon Borough Council sent an emergency waste removal operator “within 15 minutes”.
He said he also spoke to a passer-by who said she had “first noticed the bags on Wednesday, and they’d been there ever since”.
A council spokesman said: “These incidents are extremely peculiar, not to mention disturbing.
“We would like to thank the members of the public for reporting these cases to us.
“Our Highways team responded within minutes on both occasions and took the waste to our depot while we investigate who left it there.”