The Labour leader, who is an Arsenal fan, said American businessman Stan Kroenke "should stick to football if he wants to be involved in sport".
Mr Corbyn said: "I'm appalled at the glorification of killing wild and rare animals on this TV channel.
"As an Arsenal fan I'm disgusted that Stan Kroenke is involved in such a brutal, unethical and unnecessary activity.
"This is not sport. Kroenke should stick to football if he wants to be involved in sport.
"In my mind 'blood sport' is a contradiction and there should be no place on television or anywhere else for it."
My Outdoor TV was launched in the US in 2016 but has just been made available in the UK.
It operates like streaming services such as Netflix and claims to show "thousands of hunting, fishing and shooting episodes featuring the biggest names in outdoor TV" for a subscription fee of 9.99 US dollars (£7.50) a month.
A spokesman for the channel told the Independent that it will "present ethical, fair chase hunting and as long as it's legal it will be on there".
The platform is run by Outdoor Sportsman Group, which is part of Mr Kroenke's company Kroenke Sports and Entertainment.
The 70-year-old mogul owns over 67% of Arsenal, as well as the Colorado Rapids Major League Soccer team and NFL franchise the Los Angeles Rams.
Philippa King, the chief operating officer of the League Against Cruel Sports, said: "This is a massive own goal for Stan Kroenke.
"We're living in a world now where most people can see how brutal and shameful trophy-hunting is, yet the Arsenal boss is choosing to launch his sick TV channel in the UK."