Sukhumbhand — who is member of the Democrat Party which is backing the protesters — was not home at the time and no injuries or serious damage was reported.
The attack was similar to another grenade attack on the home of Abhisit Vejjajiva, a former Democrat premier whose party lost to Yingluck's in a 2011 vote.
The violence comes as Yingluck faced fresh legal troubles Friday after the country's anti-corruption commission announced it would investigate her handling of a controversial rice policy.
The legal threat added to the intense pressure against her caretaker administration to resign as protesters calling for her ouster march across the capital for a fifth day to protest at government offices.
The National Anti-Corruption Commission said Thursday that it had found grounds to investigate allegations that Prime Minister Yingluck Shinawatra was criminally negligent in her handling of what the government has described as a deal to export surplus rice to China.
The commission has already determined that there are grounds to press charges against her former commerce minister and more than a dozen other officials.
If found guilty, Yingluck Shinawatra would be forced to resign.
