It will be the first time that the Indy 500 will be run outside the month of May.
Also re-scheduled was the May 9 GMR Grand Prix, which will now be run on July 4.
Indianapolis owner Roger Penske, a legendary figure in USA motorsport for the success of his Indycar teams over the last 50 years, said: "The month of May at the Indianapolis Motor Speedway is my favourite time of year, and like our fans, I am disappointed that we have had to reschedule the Indianapolis 500".
"The health and safety of our event participants and spectators is our top priority, and we believe that postponing the event is the responsible decision with the conditions and restrictions we are facing", Penske said in a statement.
Penske Entertainment Corp. president and CEO Mark Miles added: "Memorial Day weekend has always provided Indianapolis 500 fans an opportunity to honor the men and women who have fought and sacrificed for our nation's freedom".
"We're grateful for the patience of our fans as we've navigated this situation".
Qualifying for the Indy 500 will take place on the weekend of August 15.
The Indy Grand Prix will open an unprecedented double-header featuring the first Indy road course race for NASCAR, the closed-cockpit stock vehicle series that is the most popular form of USA auto racing.
Tony Hulman bought the neglected speedway after the second war and the Indy 500 returned Memorial Day weekend of 1946 and has been scheduled for that weekend every year since.
Enhanced coronavirus safety measures will be used at the speedway, including more hand sanitizer stations, less hand-to-hand contact between fans and concession staff, more frequent facility cleaning and cleaning products that meet health expert standards for coronavirus disinfectants. It'll be the first time that the IndyCar Series and NASCAR Cup Series have run at the same facility on the same weekend and the IndyCar race will be held on the same day as the Xfinity Series race on the road course.
The postponement of the two IndyCar races at IMS means that the IndyCar Series is now set to start on May 30 with the first of back-to-back races in Detroit. Four races were initially scrapped - the street course events in the downtowns of St. Petersburg, Florida and Long Beach, California, will not be rescheduled - and IndyCar said it would resume racing 9 May on the road course at Indianapolis.