Born in Perm in 1984. At the age of four started taking music lessons with Tatyana Shevtsova, giving his first performance with an orchestra at the age of seven. Studied at the College of Music of the Moscow State Tchaikovsky Conservatoire and at the Moscow Conservatoire (class of Vladimir Ivanov). In 2012 he obtained a postgraduate degree with distinction at the Moscow Conservatoire and in 2013 another one at the Universität für Musik und Darstellende Kunst in Graz (class of Boris Kuschnir). He is currently studying at the Vienna Konservatorium. He has twice received a grant from the St Petersburg House of Music and Bank Rossiya. In 2008 he took part in a meeting of young musicians with Russian President Vladimir Putin.
Prize-winner at international competitions in Kloster Schöntal (2nd prize, 2003), Astana (Grand Prix, 2008), Seoul (2nd prize, 2012), the International Robert Canetti Competition (1st prize, 2005), the Vibrarte international competition in Paris (1st prize, 2008), the David Oistrakh Competition in Moscow (2nd prize, 2008) and the Aram Khachaturian Competition in Yerevan (1st prize, 2012). In June 2015 Milyukov won the 3rd prize at the XV International Tchaikovsky Competition.
Gives master classes in Russia and Brasil. Tours across Austria, Belgium, Brasil, China, Finland, France, Germany, Greece, Italy, Portugal, South and North Korea, Spain, Sweden and Switzerland.
Has worked with such conductors as Valery Gergiev, Vladimir Spivakov, Mikhail Pletnev, Vladimir Fedoseyev, James Conlon, Vasily Petrenko, Yuri Simonov, Pavel Kogan, Alexander Sladkovsky, Robert Canetti, Maria Eklund, and Kristjan Järvi among others. Since 2008 he has been a soloist with the St Petersburg House of Music. Since 2012 he has been a soloist with the Moscow Philharmonic. In 2016 he was awarded the Order of Friendship.
Performs the Ex-Szigeti violin crafted by Pietro Guarneri.