Kolisi had major knee surgery in April but South Africa are confident he will be fit in time for their first pool game against Scotland in Marseille on September 10th.
There are 12 World Cup debutants but the Boks kept the bulk of the side that won the tournament in Japan four years ago.
But Am, who twisted his knee in a warm-up test against Argentina on Saturday, and Pollard, who has a long-running calf injury, were among the notable omissions when the squad was unveiled at an elaborate televised ceremony named on Tuesday.
Also out is Lood de Jager, the giant lock who was also part of the team four years ago. He has an unspecific chest complaint, SA Rugby said.
"There were some tough decisions that had to be made," coach Jacques Nienaber said.
Am, De Jager and Pollard have been placed on standby with six other players and Nienaber said he was hopeful they may return to full training before the start of the tournament and be available in the event of injury to others.
"We still have two warm-up games left and a road to travel to build player combinations and fine-tune the areas of our game that we feel we need to improve on, so we are by no means the final product at this stage," Nienaber added.
Kolisi is expected to play in one of the two warm-up internationals that the Springboks will play over the next fortnight, against Wales in Cardiff on August 19th and New Zealand at Twickenham on August 25th, as he looks to prove his fitness.
He heads a list of players who compete at a third World Cup tournament. Props Frans Malherbe and Trevor Nyakane, lock Eben Etzebeth, loose forwards Pieter-Steph du Toit and Duane Vermeulen and centres Damian de Allende and Jesse Kriel are the others.
South Africa play in Pool B at the World Cup where they also meet Romania, Ireland and Tonga.
South African World Cup Squad:
Backs: Damian de Allende (Panasonic Wild Knights), Kurt-Lee Arendse (Bulls), Faf de Klerk (Canon Eagles), Andre Esterhuizen (Harlequins), Jaden Hendrikse (Sharks), Cheslin Kolbe (Suntory Sungoliath), Jesse Kriel (Canon Eagles), Willie le Roux (Bulls), Manie Libbok (Stormers), Makazole Mapimpi (Sharks), Canan Moodie (Bulls), Cobus Reinach (Montpellier), Damian Willemse (Stormers), Grant Williams (Sharks)
Forwards: Pieter-Steph du Toit (Toyota Verblitz), Eben Etzebeth (Sharks), Deon Fourie (Stormers), Steven Kitshoff (Ulster), Jean Kleyn (Munster), Vincent Koch, Siya Kolisi (both Sharks), Frans Malherbe (Stormers), Malcolm Marx (Kubota Spears), Bongi Mbonambi (Sharks), Franco Mostert (Honda Heat), Ox Nche, Trevor Nyakane (both Sharks), Marvin Orie (Stormers), Kwagga Smith (Shizuoka Blue Revs), RG Snyman (Munster), Marco van Staden (Bulls), Duane Vermeulen (unattached), Jasper Wiese (Leicester Tigers).
