Raad Harith, the deputy electriciy minister, was travelling in the eastern Baghdad suburb of Talbiya on Tuesday when at least four vehicles blocked his convoy's way, police officials said.
The gunmen, reportedly wearing security uniforms, seized the minister and up to 19 of his bodyguards.
At 7pm (1500 GMT), Harith was released with seven of his bodyguards - but he refused to say who had taken him or where he had been
Three days ago gunmen kidnapped Taiseer Najah al-Mashhadani, a Sunni legislator, and seven of her bodyguards in a northern district bordering the Sadr City neighbourhood of Baghdad.
Sunni MPs have boycotted the last two sessions of parliament, refusing to return until she is released.
Some Sunni leaders have blamed the kidnapping on Shia militias operating in the city.