Defending champion Rybakina will begin her title defence against Gauff, four-time WTA Finals participant Jessica Pegula and reigning Wimbledon champion Linda Noskova, who is making her tournament debut.
Sabalenka's group also includes 19-year-old Andreeva, 2018 WTA Finals champion Elina Svitolina and Czech Karolina Muchova.
The event, which brings together the season's top eight qualifiers, will be held at the Indian Wells Tennis Garden from November 8th to 15th. The top two players from each round-robin group will advance to the semifinals.
Rybakina, who claimed the world number one ranking after September's US Open, said the position brought both added scrutiny and motivation.
"It has been an unbelievable couple of months," Rybakina said during Tuesday's draw ceremony.
"It is of course pressure because of all of the attention, but at the same time it's motivation because you don't want to lose. In this sport, you still need to work a lot."
Sabalenka will be looking for vengeance after losing her top ranking to Rybakina at the US Open. The Belarusian won both Indian Wells and Miami earlier this year to complete the "Sunshine Double."
In July, organisers announced the tournament would move from Riyadh to Indian Wells following the early end of the WTA's hosting agreement with Saudi Arabia.