The Zimbabwe international decided to return his home country after the campaign was suspended due to the coronavirus pandemic in March.
The borders between South Africa and neighbouring countries have been closed, as part of restrictions against the virus.
Celtic media officer Sello Nduna confirmed that experienced left-back was not back at the club yet.
“The player [Pfumbidzai[ is still in Zimbabwe as there are currently no flights during the lockdown,” Nduna told Daily Sun.
The club official explained this was an issue beyond the club’s control with the Premer Soccer League (PSL) currently working with the South African Football Association (Safa) to ensure that the season resumes.
“It is difficult, therefore to say when the player will be back,” Nduna said about their first-choice left-back who has made 12 appearances across all competitions this season.
Pfumbidzai's last match for Celtic was the 5-3 defeat away to Kaizer Chiefs in a PSL encounter in December 2019, and he picked up a groin injury in the same game.
The 25-year-old has posted videos of himself training in Zimbabwe on his official Twitter account.
Meanwhile, Nduna also revealed that Celtic striker Sera Matebang is back in the country after he also travelled to his home country, Lesotho, after the season was halted.
However, the Lesotho international is still in quarantine and he is yet to link up with the rest of the players at training.
“He has been here [in South Africa] for days and has to quarantine,” Nduna added.
The 25-year-old marksman has caught the eye in his debut season in the PSL having netted four times from five starts for Phunya Sele Sele.
Matebang secured a move to Celtic from Lesotho giants Matlama FC last August after being linked with Orlando Pirates.
The hard-working frontman will be looking to continue his good form for the Free State giants when the suspended season resumes.
The PSL is hoping to complete the campaign in a Biologically Safe Environment (BSE) in Gauteng soon.