Radu's agent Ioan Becali informed Romania coach Victor Piturca that the player was quitting the national side for personal reasons.
"Mr. Becali already told you," left back Radu, who can also play as a central defender, told local media on Friday. "It's not a big loss, there are enough quality players in the Romanian team."
Radu joined Lazio from Dinamo Bucharest in 2008 and won the Coppa Italia and the Italian Super Cup the following year. In 2011, Radu signed a new five-year contract with the Rome-based club.
Radu's decision is a major blow for Piturca as he became the second Romania defender to quit the team in the last two years after Inter Milan's Cristian Chivu retired in 2011.
Controversial striker Adrian Mutu, who became Romania's all-time joint leading scorer with 35 goals last month, has criticised Radu and described his act as "disrespectful".
Romania - desperate to reach the World Cup finals for the first time since 1998 - are third in their qualifying group with 10 points from six games, eight points behind leaders Netherlands but only a point behind neighbours Hungary.