The Croatia international is almost certainly out of their visit to Manchester United on Wednesday, while Hart also has a doubt over the fitness of defender Younes Kaboul.
Portsmouth snatched their third win in eight games since Hart took over from sacked Tony Adams and, having lost only one of those, now look close to assuring their Premier League status.
The breakthrough against Bolton came after Kranjcar was stretchered off in the 75th minute after a challenge by Gavin McCann.
He appeared to be writhing in agony as paramedics arrived carrying oxygen equipment but later left the ground without the aid of crutches and Pompey will wait until Monday to give him a scan.
A downbeat Hart said: "It looks like a twisted ankle but it is still a blow for us because he's an important player for us, especially in a small-ish squad.
"I certainly wouldn't expect him to be available for the game at United on Wednesday and it could be a worry long term."
Kranjcar missed a large chunk of the season following an ankle operation in August but has returned to be a key player for Pompey.
Just two minutes after he was forced off, though, his replacement Nadir Belhadj used his first touch to fashion a viciously inswinging corner from the right and, when the ball eluded keeper Jussi Jaaskelainen, fellow substitute Kanu claimed a scoring final touch.
It was Kanu's first Premier League goal of the season and Hart said: "I didn't really see what happened for the goal but we'll take it.
"I'm told Kanu has claimed it but it doesn't matter to me who scores as long as it is us and I thought we deserved it."
Kanu, 32, has a contract which stipulates he can earn another year at the club provided he makes a certain number of first-team appearances in the current campaign.
So far he has appeared in 13 league games, mostly as substitute, and scored against AC Milan in the UEFA Cup.
Hart said: "Now is not the time to talk about contracts. We are entirely focused still on the job of staying up.
"Don't talk about systems because it is players who make systems and today I saw a very good attacking performance by us. It would not have been an injustice for us to be two or three up at half-time.
"Bolton have a way of playing that makes them difficult to play against us but I think you have to give our players credit even though we didn't dominate in the second half as much as in the first half."
Bolton boss Gary Megson did not bother to disguise his disappointment at their listless performance.
He said: "Basically we were poor and Pompey were not that much better than us but I can't think of any of our players who did as well as they are capable of doing.
"We've got to show a big improvement on this even though three of our last five matches are at home. We are certainly not thinking we are safe yet."
After a hat-trick of first-half saves - all to deny man of the match Glen Johnson - Jaaskelainen must share blame for Pompey's winner.
But Megson said: "The defending for the corner was very bad, letting it go straight in like that from Belhadj's corner.
"Did Kanu claim it? Well, he would. I should know, having had him at West Bromwich Albion!"