Police launched the search for the goats after the MP's brother filed a complaint of theft.
Police said the thieves may have abandoned the goats and fled after they were spotted by some villagers while leading the herd.
The police in Vidisha, located about 50 kms from the state capital Bhopal, swung into action immediately after Salim's younger brother Mubassar Chowdhary lodged the complaint on Monday.
"Mubassar Chowdhary, the younger brother of Rajya Sabha member Munawwar Salim, registered a complaint that 23 goats went missing from their farm at Berkhedi on Sunday night. We recovered 17 of them within 24 hours," Vidisha's Civil Lines police station in-charge H S Rajawat told PTI.
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The goats were found in a forest in Murwara village, about eight kms from the farm, said Rajawat, who led the search team.
"We were able to trace 17 goats from the forest near village Murwara on Tuesday evening. The carcasses of three goats were found in the area. It seems that dogs killed them. Now, only three goats are missing," he said.
Appreciating the swift action by police, Chowdhary thanked the City Superintendent of Police Nagendra Pateria.
The MP said he was fond of rearing goats and dogs.
"These are Alwari goats, which are very young and beautiful. The police and people helped a lot to track them. The person who stole them must also be fond of rearing. I am happy that most of them were finally found," Salim added.
Notably, in 2014, seven buffaloes were stolen from a barn owned by SP leader Azam Khan in Rampur district of Uttar Pradesh, following which dog squads, crime branch sleuths and police personnel were put on the job to find them.