The Taliban claimed to have kidnapped both men and said on Saturday afternoon the Indian man would be killed unless India withdrew all its workers from Afghanistan in 24 hours.
The Taliban also claimed it had shot dead the Indian hostage after he tried to escape.
Ghulam Nabi Malakhail, police chief of Zabul province, said a highway police patrol found the body near the Hassan Kariez district of Zabul, the same area where Indian hostage K. Suryanarayana was abducted on Friday.
"We are investigating whether the body is that of the Indian hostage," Malakhail told reporters.
Qari Yousuf Ahmadi, who releases regular statements on behalf of outlawed Taliban fighters, said militants shot the Indian after he tried to escape and fought with his captors.
Indian officials were not immediately available for comment.
Ahmadi issued a threat on a day earlier saying all Indians must leave Afghanistan by 6 p.m. (1330GMT) on Sunday or the Indian telecommunications engineer would be executed.
Suryanarayana, a father of three from Hyderabad aged in his early 40s, had been employed in Afghanistan since January by a Bahrain-based company, Al Moayed.
The company has been contracted by an Afghan mobile phone company, Roshan, to expand its mobile phone network across volatile provinces in southern Afghanistan.
His kidnapping is the first since four Macedonians of Albanian descent were kidnapped and killed in March, purportedly by Taliban militants.