The British sportscar company is controlled by Canadian billionaire Lawrence Stroll, owner of the Racing Point F1 team, which will be rebranded as Aston Martin in 2021.
Wolff has bought a stake of just under 5%, which will become 0.95% after a rights issue in Aston Martin on Monday.
A Mercedes spokesman said the move did not affect Wolff’s role as an executive and shareholder at Mercedes F1.
He said Wolff’s purchase was “a financial investment”.
Stroll’s takeover of Aston Martin was approved by shareholders earlier this month. He became executive chairman after injecting £260m of new capital.
Wolff has bought nearly 14.5m shares. The current market price of Aston Martin shares is 55p, giving him a shareholding worth £7.975m at today’s prices.
Wolff owns 30% of the Mercedes team and is in negotiations with Ola Kallenius, chairman of parent company Daimler, about an extension of his contract beyond the end of this year.
Daimler is also a shareholder in Aston Martin, having taken 5% of shares in 2013 in return for supplying engines and electronic components.
Wolff was forced to divest himself of a previous shareholding in Williams when he joined Mercedes in 2013.
But Daimler does not see Wolff’s shareholding in a company that by next year will have its own works F1 team as a conflict of interest because it sits along its own.
The Mercedes F1 team also have engine and gearbox supply and technical co-operation agreements with Racing Point.
The investment has been approved by the relevant compliance bodies within Daimler.
Despite Daimler’s position, the move will inevitably raise questions among other F1 teams, some of whom are uncomfortable about the apparent closeness of Mercedes and Racing Point, and of Wolff and Stroll as personal friends.
A number of other teams regard Racing Point as an effective Mercedes B team, and many were angered when they saw the similarity between this year’s Racing Point car and last year’s Mercedes.
Racing Point insist they have simply copied the 2019 Mercedes, something any other rival could have done, and it made sense for them to do so given they buy so many parts from the world champions.