Levon started dating Australian Woman International Master Arianne Caoili in 2008. The two announced their engagement in February 2015 and got married on 30 September 2017 in Yerevan. They had first met at the 1996 World Youth Chess Championships in Las Palmas and began a friendship in 2006, when their mutual friend International Master Alex Wohl reintroduced them in Berlin. On 30 March 2020, Aronian revealed on his Twitter account that Caoili had died. The Philippines-born former model had succumbed to serious injuries sustained two weeks earlier in a car crash.