Kucera, who has won two tournaments this year and was a finalist in Vienna three weeks ago, has qualified for the first time for the $3.5m (pounds 2.1m) eight-man event, which takes place from 24 to 29 November.
With world No 3 Patrick Rafter, of Australia, and the Dutchman Richard Krajicek, ranked ninth, pulling out through injury, Kucera's position is safe, with two places remaining to be filled. These will be decided at the Stockholm and Moscow tour events this week.
Britons Tim Henman and Greg Rusedski, the winner of Sunday's Paris Open final against the American world No 1 Pete Sampras, are the favourites. Both are playing in Stockholm.
Krajicek, a former Wimbledon champion, underwent surgery on his left knee yesterday in Rotterdam. The Dutchman missed several tournaments this season because of a torn cartilage.
Krajicek won a tournament in Stuttgart eight days ago and was in line for a place at the World Championship, but he withdrew from the Paris Open for treatment on his knee when leading Switzerland's Marc Rosset in a second-round match last Wednesday and decided his season was over.
Peter Vergouwen, of the Utrecht University Hospital AZU, who is supervising Krajicek's recovery, said the player was aiming to return to competition in a tournament in Sydney, which starts on 11 January.
The fourth-seeded Byron Black, of Zimbabwe, defeated Martin Damm, of the Czech Republic, in straight sets in the first day of play in the Kremlin Cup yesterday.
Black, ranked 28 on the ATP Tour, was the only seed to play yesterday. He overcame Damm 6-2, 6-3.
The ninth Kremlin Cup tournament will see only three players from the top 15: the No 6, Alex Corretja of Spain, the defending champion, Yevgeny Kafelnikov, and the 1996 Kremlin Cup winner, Goran Ivanisevic of Croatia, who was granted a wild card for the tournament.
Guillaume Raoux, of France, defeated Ukraine's leading player, Andrei Medvedev, yesterday in two sets 7-6, 6-4, while Sjeng Schalken, of the Netherlands, outplayed the Russian doubles specialist Andrei Olhovskiy 7-5, 6-4. But Olhovskiy, 32, a wild card entry, was playing in only his second singles tournament this year.Reuse content