Caroline Lucas has reported a tweet published by Brexit moneyman Arron Banks
The Leave.EU founder responded to a post by Green party MP Caroline Lucas about Greta's voyage across the Atlantic on a racing yacht, writing: "Freak yachting accidents do happen in August ..."
He later tweeted that it was a "joke" after his comment sparked outrage from social media users.
Ms Thunberg, who chooses not to fly, is sailing from the UK to attend UN climate summits in New York and Chile.
Ms Lucas said she reported his comment.
"Arron Banks' vile tweet about @GretaThunberg makes me sick to the stomach," Ms Lucas wrote on Twitter on Thursday morning.
"I have made a formal complaint to Twitter."
Among those to criticise Mr Banks post was actress Amanda Abbington, who tweeted: "You're wishing a potentially fatal accident onto a sixteen year old girl, why..?"
She had earlier written: "If you are a grown up, fully-fledged adult and you are mocking this young girl for trying to save the planet then I genuinely feel sorry for you."
One Twitter user responded to Mr Banks' post by saying: "You know she's 16, right?" while another described his comment as "despicable".
Mr Banks later defended his post and, in response to another tweet which highlighted the fact Greta was a child, he said: "Quite and one being used. Obviously I don't hope she encounters a freak yachting accident! I just enjoy watching the ludicrous tweeter mob following the next outrage ..."
He also replied to someone accusing him of showing "his true colours", saying: "It was a joke .. you lefties have no sense of humour ..."
Greta is embarking on a two-week voyage across the Atlantic on a carbon-neutral racing yacht, the Malizia II, so she can attend high-profile climate events without using planes or cruise ships which emit greenhouse gas emissions.
The Swedish teenager's "school strikes" have inspired a global protest movement by young people demanding urgent action on climate change.
