The star, who is the son of actors Will Smith and Jada Pinkett Smith, is also an investor in plant-based startup Impossible Foods.
"Dear Meat Eaters Let's Start Doing #MeatlessFridays Where We Don't Eat Meals That Include Meat For The Entire Day," Jaden said.
The tweet received more than 31,000 likes and 6,400 retweets - with many fans approving of the initiative.
One user commented: "This is such a good way of helping and possible for me without shaming meat-eaters who can't necessarily stick to vegan diets because of health issues."
Vegan food truck
The 'I Love You' eatery was brought to the Skid Row area, which has one of the largest homeless populations in America.
Jaden shared the news about the truck on Instagram, posting a photo and writing: "I Love You Restaurant is a movement that is all about giving people what they deserve - healthy, vegan food for free.
"Today, we launched our first one-day food truck pop-up in Downtown LA. Keep a lookout because this is the first one of many."