The MLS expansion franchise will make the upper level available for the June 28 meeting with their New York rivals which will be the second derby after the Red Bulls play host at Red Bull Arena this weekend.
NYCFC president Tom Glick said in a statement: "The atmosphere at our home games has been fantastic all season.
"When we were looking at this game on June 28 being on the verge of selling out this far in advance, we made the decision to open up more seats to accommodate the demand. We are pleased with the momentum we have had in tickets sales and that so many New Yorkers continue to get behind our Club in our inaugural season."
City have played five home matches at Yankee Stadium in their inaugural MLS campaign, attracting a high of 43,507 in their season home opener against New England Revolution on March 15 (2-0 win), and a low of 20,461 against Philadelphia Union in April (1-1 draw).