The 24-year-old Togo international midfielder, who has struggled to make an impact with the Pilgrims since joining from Sheffield Wednesday in January 2008, started the clash against the South West Peninsula League side.
But Folly lasted just 18 minutes before limping out of the action.
Argyle boss Paul Sturrock said: "It's a bad blow. He got a kick on the ankle, so I don't know how long it will be that he's out.
"There was no malice in the tackle. It was just one of those unfortunate things."
Simon Walton, who had played at right-back 24 hours earlier in the 2-0 win at Truro City, was given another run-out, this time at centre-back.
However, he sustained a thigh strain and may now be rested for the rest of the week.
An otherwise young Argyle side went behind early on to Parkway, Andy Sergent scoring after just two minutes, but were on level terms through Joe Mason's penalty on 22 minutes.
After the break, a fine lob from Matt Rickard (54) put the visitors in front and Republic of Ireland youth international Mason - recently promoted to the senior ranks - bagged a second goal on the hour mark with a cracking volley.
Argyle play their third game in three days against Torquay United at Plainmoor on Wednesday night.