A senior police official identified the deceased as S Periyapandiyan, an inspector attached to the Maduravoyal police station in Chennai.
"The shoot-out took place when a police team went to nab the suspects at a village in Pali district. Periyapandiyan was killed in the firing while others suffered injuries," he said.
The incident occurred around 2:30 am, the official said.
A police team led by Joint Commissioner (West) Santosh Kumar is likely to visit Rajasthan in connection with the incident.
Special teams were formed to nab the robbers, who were suspected to be from Rajasthan.