Iran-aligned Houthi forces in Yemen have been attacking maritime traffic in what they say is a response to Israeli military action in Gaza.
The authorisation would provide for up to 700 German military personnel to take part in the mission to protect shipping in the Red Sea.
German Vice-Chancellor Robert Habeck said he does not expect major supply chain problems for the German economy.
The price of oil rose sharply on concern that supplies could be disrupted. Brent crude rose $2.
It took about one million Egyptians and 120,000 deaths to put the Suez Canal in place in 1859.
