BMW, Daimler and Volkswagen , which all have plants in Mexico, taking advantage of lower labour costs and the U.S.'s trade deals with its southern neighbour, were down by up to 2.3 percent at 0700 GMT.
Shares in Asian auto makers dropped overnight.
Trump said he would hit all goods coming from Mexico with a 5% tariff, adding that he would hike that further each month until it hit 25% on Oct. 1, unless Mexico takes immediate action against illegal immigration across the U.S. border.