"The reality is that we will be unwelcome guests in a country seized by fanatics, who dream of destroying all the good between the Russian and Ukrainian peoples," he wrote, according to BBC News.
Channel One has yet to respond.
In an interview with the BBC, Mr Milonov claimed that "many Russians" backed his call. He accused the Ukrainian authorities of supporting "right-wing fascist bandits" and proposed renaming Eurovision in Kiev "Reich-vision".
Mr Milonov suggested that supporting Eurovision there would be "the same as supporting the fascist Olympic Games of 1936 in Berlin".
Read alsoO.Torvald to represent Ukraine at Eurovision 2017 (video)The MP received support from fellow-parliamentarian and veteran variety singer Iosif Kobzon.
Kobzon, sometimes referred to as "Russia's Frank Sinatra", told the Tass news agency: "I'm categorically opposed to performing in front of an audience that will spread Russophobia.
"We must ignore this festival. It's taking place in a country which is killing people in the Donbas."
Comments like these have sparked indignation in Ukraine.
"Such aggressive rhetoric from the Russian authorities is strange," says Ukrainian MP Olga Chervakova, deputy head of the Ukrainian parliament's Committee on Freedom of Speech.
"On the other hand, it is logical. For some time now Russian officials have been boycotting many things: in the UN Security Council, Russia has been boycotting common sense, in Crimea and the Donbas, Russia has been boycotting international agreements, while at home [with anti-EU sanctions] it's boycotting Swiss cheese."
The Kremlin appears to be hedging its bets.
"It's not clear whether we need to boycott," President Vladimir Putin's spokesman Dmitry Peskov told the BBC. "Of course, considering where this competition is taking place, and the possible problems with security and unfriendly attitudes, there is an obvious cause for concern. But, as far as we know, no decision has been taken."
Read alsoUkraine shrugs off threat to Eurovision after resignationsUkrainian MP Olga Chervakova dismisses suggestions that Russians traveling to Eurovision in Kiev would be putting themselves in danger.
"If anyone should be frightened, it's the Ukrainians," Ms Chervakova told me by telephone. "We call Russia an aggressor... But we can separate the Russian authorities from ordinary Russian citizens. They have nothing to fear."
Ms Chervakova says she has a message for Moscow if Russia decides against a boycott: "If Russia does take part, I'd ask the Russian delegation to come here without 'little green men' or the kind of props we see in the Donbas: heavy-calibre mortars."
"Little green men" was the nickname given to soldiers in unmarked uniforms who seized Ukraine's key installations in Crimea in 2014, paving the way for Russian annexation.