MUMBAI—Indian police arrested 17 men they say are members of a fringe Hindu nationalist group on suspicion of killing a Muslim computer engineer, in a case that has renewed concerns about religious violence in the world's largest democracy.

Police said the men beat to death 28-year-old Mohsin Sadiq Shaikh in the western city of Pune because he was Muslim. The attack happened Monday night after days of anti-Muslim incidents, said Additional Commissioner of Police Abdur Rehman. "He was a poor man, returning home after performing...