The 22-year-old forward joined Celtic in January this year but is yet to carve out a niche for himself in the team.
He has been a bit part player at Celtic this season under Brendan Rodgers and has only made one league start in the entire campaign thus far.
There are suggestions that he could be moved on in the winter transfer window as Rodgers looks to bring in more players to further strengthen his Celtic squad.
Hartson stressed that a Celtic forward needs to be well-rounded and should have all the characteristics needed to lead the line at Parkhead.
The former Celtic star is still not sure that Oh has it in him to be a Celtic striker given what he has shown so far in a Bhoys shirt.
Hartson said on the Go Radio Football Show: “It’s not a criticism of him, but I still think as a Celtic centre-forward, he has to be able to get goals, hold the ball up, head the ball, take you up the pitch, go and attack it in both the boxes.
“That’s how I see it.
“Whether he has got all those tools, I don’t know.”
Oh has scored three times in 12 appearances in the Scottish Premiership so far this season and will look to impress over the busy Christmas period.