Occupants of the vehicles got out and separated the two men.
Washington County court records show Ramsey was released Sunday on US$11,085 ($18,800) bond. A court appearance is scheduled for October 19.
Ramsey, 53, spent more than 30 years at Springdale, Arkansas-based Tyson Foods before joining Beyond Meat as chief operating officer late last year. He held top leadership positions at Tyson, including president of its poultry division and president of its global McDonald's business.
At Beyond Meat, he has guided partnerships with fast food companies including McDonald's and KFC.
Beyond Meat didn't respond to email and telephone messages left by the Associated Press.
Beyond Meat shares fell 2 per cent Tuesday to US$16.68, close to their 52-week low of US$16.51.
The El Segundo, California-based company has been struggling this year as customers dealing with soaring grocery bills have bypassed its higher-priced vegan products. McDonald's also recently ended a US trial of its McPlant meatless burger - developed with Beyond Meat - without confirming any future plans for the product.
Beyond Meat laid off 4 per cent of its workforce last month.