The collection of paintings by celebrated Austrian artists including Oskar Kokoschka and Koloman Moser was valued at more than €2 million.
The 73-year-old owner was on holiday when her house in Hietzing was broken into in late August.
She initially reported that 71 works of art were missing but has since discovered that one more piece was taken.
The reward has been provided by an anonymous donor and the full amount will only be given if all 72 paintings are found. If only some are found, then a partial reward will be given.
Police said the reward was the highest that has ever been offered in Austria after such a theft, and that the Federal Police would only be involved as a coordinator and mediator, with the anonymous donor responsible for all details pertaining to the reward.
Interpol has launched an international search for the paintings.