The purchase, expected to be finalised this week, will reduce Renova's stake in Sulzer to below 50 percent, the company said in a statement.
"Sulzer is in close contact with authorities and believes that this transaction will assuage any concern as to the independence of Sulzer from the Renova Group," it further said.
Sulzer, which specialises in industrial pumping systems, acknowledged that Vekselberg had been designated on a US sanctions list and said it agreed to the share buyback with Renova "to minimise disruptions to Sulzer's business."
The precise value of the deal is not yet clear.
Sulzer said it would sell the shares based on a "volume-weighted average" of its share price between Monday and Friday.
Sulzer was trading down 9.3 percent on Monday, at 114.30 Swiss francs ($119.10, €0.97).
But the company also said it would not transfer any funds to Renova until "Sulzer has obtained legal confirmation that such transmission does not expose Sulzer to the risk of primary or secondary sanctions."
Washington on Friday unveiled a range of sanctions targeting Russian President Vladimir Putin's inner circle.
President Donald Trump's administration has said the measures were aimed at punishing Russia for a range of actions, including election interference and support of the Syrian government.
The measures targeted seven oligarchs, 12 companies they own or control, 17 senior Russian officials and the state-owned arms export company