Monia has also been a member of the senior Russian national basketball team. With the Russian national team, he played at the EuroBasket 2003, the EuroBasket 2005, the 2008 Summer Olympics, the EuroBasket 2009, the 2010 FIBA World Championship, the EuroBasket 2013, and the EuroBasket 2015. He also won a gold medal at the EuroBasket 2007, a bronze medal at the EuroBasket 2011, and a bronze at the 2012 Summer Olympics.