The Soyuz capsule had been used to deliver a new crew to the laboratory 400km (250 miles) above the Earth in June.
The hole had to be examined in space, because it was located in the section of the spacecraft that would separate during the reentry and burn in the atmosphere, making further investigation impossible.
Prokopyev and Russian Oleg Kononenko had to use a pair of telescoping booms to reach the Soyuz.
An air leak coming from the Soyuz module led astronauts to find a 2mm hole, one that was conclusively not made by a micrometeorite and was determined to be done over the course of several attempts by someone with a "wavering hand", according to Dmitry Rogozin, the head of Russia's space agency.
Prokopyev, who's been on the station for six and half months, will use the MS-09 he's investigating Tuesday to return to Earth with the European Space Agency's Alexander Gerst and NASA's Serena Aunon-Chancellor on December 20.
Unlike the ISS, the spacecraft is not created to be repaired in space and has no railings or anything to cling on to from the outside.
The hole was in the orbital module, also known as the habitation module - one of three modules on the Soyuz vehicle.More news: Faulty tampons recalled across Canada, U.S.
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The Soyuz spacecraft is used to ferry astronauts to and from the ISS.
After more than five hours of a rare broadcast - showing the cosmonauts in space trying to cut through an insulate of the spacecraft with a knife - they uncovered the external part of the hole, originally discovered in the capsule's internal covering, and took samples of the exterior insulation.
This was the 213th spacewalk in 20 years at the space station. Astronauts Sergey Prokopyev and Alexander Gerst repaired the 0.07-inch-wide (2 millimeters) hole with material soaked in an epoxy sealant.
The spacewalk was the fourth for Kononenko and the second for Prokopyev.
"The active participation of worldwide partners, primarily NASA, in the investigation is not expected, although we have called for a joint investigation and been ready to provide available materials: photos, videos, documents, samples of materials taken during the spacewalk", the source said.
The insulation proved harder to remove than expected.
The samples, data and photographs taken from the leak site will be brought back to Earth and analyzed by Russian specialists.