Steinbrenner died Tuesday of a heart attack at the age of 80. Sheppard, 99, died last Sunday.
The Yankees said video tributes for both Steinbrenner and Sheppard would be shown prior to Friday's game against Tampa Bay. There will also be moment of silence for both men. The game against the Rays will be the first for the Yankees after the All-Star break.
A wreath will also be placed in front of Steinbrenner's statue outside Yankee Stadium.
In addition, the team said more than 40 former players and coaches would be present for the 64th old-timers' day Saturday.
Steinbrenner purchased the Yankees in 1973 and since then they have won 11 American League pennants and seven World Series titles.
Sheppard was the team's public address announcer for 56 seasons beginning in 1951.