Brown pleaded no contest, an admission of guilt under California law, to driving under the influence and driving on a suspended license in October in a Los Angeles suburb.
Police said they stopped Brown after seeing him driving erratically, and that he failed a field sobriety test. It was his second arrest for drunken driving in 2012.
Brown did not appear in court on Tuesday and his plea was entered by his attorney. He must report to jail on March 20
The New Edition singer was also sentenced to four years probation, ordered to install an ignition interlock device and to attend an alcohol counseling program.
Brown and Houston divorced in 2007 after 15 years of what Houston later described as a drug- and alcohol-fueled marriage. Houston drowned accidentally in a Beverly Hills hotel bathtub on February 11, 2012, from the effects of heart disease and cocaine.
(Reporting By Jill Serjeant; Editing by Doina Chiacu)