They suspect that the money came from the proceeds of a crime.
Three young men who saw the cash in the water on Saturday, stripped and jumped in to collect it before police arrived and gathered up the rest.
Police spokesman Johann Baumschlager told the Kurier newspaper that a man had been arrested in Lower Austria in connection with the money, but said he couldn't provide further details as the investigation is ongoing.
Police insiders have said that it's believed the suspects threw the money into the river in a moment of panic, and that the cash may have come from a money laundering deal.
Under Austrian law anyone who finds money and hands it into the police can keep up to 10 percent as a reward, but if it can be proved that it is the proceeds of criminal activity the young men are unlikely to get a finder's reward.
The students also failed to call the police when they spotted the money floating in the river - which means they could even face a fine.
Police were alerted by a passer-by who thought the young men were attempting suicide by jumping in the water.