El Aissami said authorities arrested four of the captors, all of them Venezuelan men in their 20s. A 60-year-old woman and a 74-year-old man were also arrested as accomplices for supplying the kidnappers with food.
Authorities were still searching for four Colombian men who escaped during the rescue, El Aissami said. He didn't say whether anyone was wounded in the gun battle.
Ramos, 24, was seized at gunpoint outside his family's home Wednesday night and whisked away in an SUV.
El Aissami said investigators' first break in the case came when they found the kidnappers' stolen SUV abandoned in the town of Bejuma alongside the mountains of central Carabobo state. With that location pinpointed, he said, they studied past crimes in the area and ended up checking on a rural house that authorities believed had been used in a previous kidnapping.
El Aissami said authorities took over the house and detained the couple who had been cooking for the abductors, who were holding Ramos in another house in the area.
Ramos had recently returned to his homeland after his rookie year with the Nationals to play during the offseason. When he was abducted, he was standing with his father and two brothers just outside the front door of his family home in a working-class neighborhood of Valencia, about 90 miles west of Caracas.
Ramos said his captors bound his hands at first, but later allowed him not to be tied up. The kidnappers didn't cover their faces and they spoke little to him, he said. "They demanded only money."
Ramos said he was kept in a room and passed the time lying on a bed. When the gunfire erupted Friday as his rescuers arrived, "I was on the bed and I threw myself directly to the floor."
Ramos said he was enjoying being back with his family, and planned to start training Monday to play with his Venezuelan team, the Aragua Tigres, on Wednesday.
Nationals general manager Mike Rizzo celebrated the news.
"He asked me to thank all who played a role in his rescue, and all those who kept him and his family in their thoughts and prayers," Rizzo said. "I join Wilson in thanking the many law enforcement officials in Venezuela and investigators with Major League Baseball who worked tirelessly."
Security has increasingly become a concern for Venezuelan players and their families as a wave of kidnappings has hit the country's wealthy and middle class in recent years. Venezuela has one of the highest murder rates in Latin America, and the vast majority of crimes go unsolved.
MLB officials said it was the first kidnapping of a major leaguer that they could recall. But relatives of several players in Venezuela have previously been kidnapped for ransom, and in two cases have been killed.
Bodyguards typically shadow major leaguers when they return to their homeland to play in Venezuela's baseball league.
"They didn't physically harm me, but psychologically I underwent very great harm," Ramos said. "I was always praying."