Djokovic has been transferred to Melbourne's Park Hotel, a detention facility for refugees and asylum seekers, after his visa to enter Australia was blocked.
Prime Minister Scott Morrison said this week that Djokovic, who hasn't publicly revealed his vaccination status, "didn't have a valid medical exemption" to the vaccination requirement for arrivals into Australia.
"Look I definitely believe in taking action, I got vaccinated because of others and for my mums (sic) health, but how we are handling Novak's situation is bad, really bad," Kyrgios wrote on Twitter on Friday.
"Like these memes, headlines, this is one of our great champions but at the end of the day, he is human. Do better."
World No. 93 Kyrgios, never shy to speak his mind, has previously been critical of Djokovic's behavior during the pandemic -- notably during the ill-fated Adria Tour event in 2020 which saw a number of players, including Djokovic, test positive for Covid-19.
In November, Kyrgios said he didn't think anyone should be forced to get vaccinated, but later added that it would not be "morally right to accept players from overseas that aren't vaccinated" into Australia.
Djokovic, currently tied with Roger Federer and Rafael Nadal on 20 grand slam singles titles and hoping to win his 10th Australian Open title in Melbourne, also received support from fellow player John Isner while the debacle about his visa continues.
"What Novak is going through right now is not right," Isner wrote on Twitter. "There's no justification for the treatment he's receiving. He followed the rules, was allowed to enter Australia, and now he's being detained against his own will. This is such a shame."
Nadal, meanwhile, was less sympathetic towards Djokovic: "He made his own decisions, and everybody is free to take their own decisions, but then there are some consequences," the Spaniard told reporters in Melbourne on Thursday.
"Of course, I don't like the situation that is happening. In some way, I feel sorry for him. But at the same time, he knew the conditions since a lot of months ago, so he makes his own decision."
Djokovic's legal team has sought an urgent injunction against the decision to revoke his visa while he continues to be held in Melbourne. The country's Federal Court has adjourned the decision until Monday on whether he will be allowed to remain in Australia or be deported, according to Reuters and public broadcaster ABC.
On Friday, Australia's home affairs minister Karen Andrews said Djokovic is "not being held captive" in the country.
"He is free to leave at any time that he chooses to do so, and Border Force will actually facilitate that," Andrews told ABC. "It is the individual traveler's responsibility to make sure that they have in place all the necessary documentation that is needed to enter Australia."
Andrews' comments came after Djokovic's family members back home in Serbia had protested against the actions of the Australian authorities.
"They are holding him captive. Our Novak, our pride. Novak is Serbia, and Serbia is Novak," Djokovic's father, Srdjan, said on Thursday.
"They trample Novak, and so they trample Serbia and the Serbian people ... They wanted to underestimate him, to bring him to his knees, and not only him, but also our country, our beautiful Serbia.
"We are Serbs, proud European, civilized people. We never attacked anyone, we just defended ourselves."
Djokovic's wife, Jelena, took a more mild approach as she spoke publicly about the situation for the first time on social media: "I am taking a deep breath to calm down and find gratitude (and understanding) in this moment for all that is happening," she wrote on Instagram.
"The only law that we should all respect across every single border is Love and respect for another human being."
CNN's Sophie Jeong, Niamh Kennedy, AnneClaire Stapleton and Jessie Yeung contributed reporting.