The car of Brazil's Mario Moraes span and crashed on the back of Andretti's slowing car as they approached the first chicane after the start.
It took more than five minutes for officials to remove Moraes' car so the medical team could attend to Andretti, who eventually was able to walk away from the scene.
Andretti was briefly taken to the medical center and then released.
The American driver said he slowed down because he could not see in front of him as other drivers made contact approaching the first turn and threw a lot of dust into the air.
"It's obviously dusty," he said. "I think if you have any common sense, you're not going to stay flat out if you can't see the car ahead of you."
Moraes also said he couldn't see much.
"The drivers were forced to brake before they were used to," he said. "It was a shame that this happened."
There was extra dust at the Sambadrome straight because officials had to add grooves to the concrete surface overnight after drivers complained that the track was too slippery and unsafe.
The track was washed several times, but they could not remove all of the dust ahead of the race.
Former Formula One driver Takuma Sato, Scott Dixon, three-time Indy 500 Helio Castroneves and Ryan Briscoe also were involved in accidents at the beginning of the race.
Danica Patrick, Milka Duno, Mario Romancini, Alex Lloyd and Hideki Mutoh also fell down the race order after incidents at the 2.6-mile, 11-turn Anhembi street circuit in South America's biggest city.