The 34-year-old defender tore a cruciate ligament against Wolverhampton Wanderers in March and will not go to North America with the squad for their pre-season trip.
“Sol is doing well, but if he plays much before September, I’d be surprised,” manager Neil Warnock stated.
“The time frame should be early October.”
He continued: “He’s doing so well it might not be that long, but I wouldn’t expect him back too early.”
Bamba, who has a year left on his Cardiff contract, featured in all but one of the Bluebirds’ Premier League games before being injured, his absence a blow in Warnock’s ultimately unsuccessful bid to avoid relegation.
Following ankle surgery, Scotland international Callum Paterson is in contention to start the Championship campaign.
Paterson, like Bamba, will miss the trip to North America.
Cardiff suffered the loss of versatile Paterson in April after he injured his ankle during Scotland’s Euro 2020 qualification triumph against San Marino.
Warnock believes the club’s three-game tour to the United States and Canada has “come too soon” for the 24-year-old, who will return to the first-team squad.
Paterson could return in time for the season opener against Wigan on Saturday, August 3rd.
Joe Ralls, who missed the final three games of the season due to a hamstring injury, is back in full training.
Cardiff will also be without midfielder Lee Tomlin and striker Gary Madine for the tour because of visa issues.
They will instead join the club’s Under-23 squad for games in Devon and Cornwall, led by first team coach Ronnie Jepson.
Cardiff travel on Thursday to take on USL Championship teams San Antonio and New Mexico before facing Spanish La Liga side Real Vallodolid in Edmonton, Canada.
Warnock added: “Things have gone well so far. The lads worked hard last week and now it’s about getting games under their belts. I’m looking forward to it.”
