Fijian social media has been buzzing with rumours that Bainimarama's health has deteriorated after undergoing heart surgery at a Melbourne hospital last month.
But democracy advocate Pita Waqavonovono said Fijian citizens deserved to know the health status of the leader of the country.
He said the government's decision to remain silent did not help quell such rumours.
"So, the problem here is that all this energy placed on trying to portray positivity, distract and shape opinions is actually met with a question - update us. Is he alive? How can we help? Nothing is coming to us through the traditional forms so social media has taken over that void."
RNZ Pacific has contacted Fiji's information department for comment.
The government announced last month that the prime minister was recovering from cardiovascular surgery in Melbourne, Australia.
At a media conference on 15 January, acting prime minister Aiyaz Sayed-Khaiyum said Bainimarama was not expected to return to work until the end of February.
Sayed-Khaiyum said Bainimarama was in high spirits and had spoken with his family.
"Per the doctor's orders, this type of surgery takes weeks, at a minimum, to recover from. So, we expect to have our prime minister back at the helm of the nation, fitter than ever, by the end of the next month [February]," he said.
Sayed-Khaiyum said he was in Singapore for a medical check-up late last year.