As it stands, the only way to watch the broadcast of the game against the visiting Boston Red Sox is on streaming service Apple TV+.
"History is in the making as Aaron Judge electrifies Yankees fans, and everyone who loves baseball," James said in a release.
"To deny millions of New Yorkers, and fans around the nation, the opportunity to watch as Aaron Judge steps up to the plate, is wrong and unfair.
"That is why I am calling on Apple and the MLB to reach a fair accommodation with the YES Network so that fans can watch what we all hope will be history made this evening."
YES primarily serves New York City and the surrounding areas.
An MLB spokesman did not have any immediate comment on the request but in a news release this week about the Yankees broadcast schedule, MLB noted that Friday Night Baseball on Apple TV+ is free and available to anyone with internet access across devices where Apple TV+ can be found.
Apple did not immediately respond to a request for comment from Reuters.
Judge hit his Major League-leading 60th home run on Tuesday, tying the mark set by Yankees great Babe Ruth, and is now one big swing shy of Roger Maris's 61-year-old American League record for home runs in a single season.
