"I am so concerned about Lewis. Hope he is ok," a fan wrote.
"Please don't give up on the world. There are people that care, whilst the world may seem c**p at times you have to look for the positives. I promise you there are some," another added.
Hamilton, who leads the Formula One season by 64 points with four races remaining, became the sports highest paid driver last year with nearly US$500m in career earnings, according to Forbes.
Hamilton went vegan two years ago and recently opened a vegan burger restaurant to help reduce greenhouse emissions created by livestock.
"I stopped eating red meat two years ago, I have generally been pescatarian for the majority of the year and now I've cut fish," he told the BBC.
"As the human race, what we are doing to the world... the pollution [in terms of emissions of global-warming gases] coming from the amount of cows that are being produced is incredible.
"They say it is more than what we produce with our flights and our cars, which is kind of crazy to think, the cruelty is horrible and I don't necessarily want to support that and I want to live a healthier life."