President Donald Trump would certainly be facing a “real trade war” if he were to implement tariffs on European cars and SUVs being imported into the United States, AutoNation Chairman and CEO Mike Jackson told CNBC on Wednesday.

"Automotive tariffs will make steel tariffs look like a company picnic," said Jackson, head of the nation’s largest auto retailer. "This will unleash, if it comes about, a real trade war because the numbers are just so much bigger. It will raise prices dramatically for consumers in the United States. It will be inflationary."

Jackson was reacting to the president’s tweet last week, threatening the European Union with auto tariffs if it does not drop its tariffs on certain U.S.-made products, including bourbon and motorcycles. Those were in retaliation for Trump's levies on EU steel and aluminum.

Based on the Tariffs and Trade Barriers long placed on the U.S. & its great companies and workers by the European Union, if these Tariffs and Barriers are not soon broken down and removed, we will be placing a 20% Tariff on all of their cars coming into the U.S. Build them here

Jackson said Wednesday on “Squawk Box” that tariffs on European automakers don’t make any sense because they're already investing in America, pointing to the expansive BMW, Mercedes and Volkswagen plants in the U.S.

"So you want to punish them for doing what you want? That's where it gets to be a little bit of a head-scratcher," the AutoNation CEO said.

Trump told automakers at a meeting in the White House on May 11 that he was planning to impose tariffs of 20 percent or 25 percent on some imported vehicles, and sharply criticized Germany’s automotive trade surplus with the U.S.

On Wednesday, the Alliance of Automobile Manufacturers, a trade group representing domestic and foreign automakers with plants in the U.S., predicted the average price of a new vehicle would increase $5,800 if the president imposes a 25 percent tariff on imported models. That would amount to a $45 billion tax on the auto industry and ultimately lead to American job cuts, according to the trade group’s letter to the Commerce Department.

Commerce is currently investigating whether auto-related imports are a threat to national security. If they are deemed a threat, it would give Trump the justification he needs to impose tariffs on imported autos.

The White House did not immediately respond to a request for comment.

— CNBC's Phil LeBeau and Reuters contributed to this report.