"Get well soon, Tiger. You are a true champion," Mr Trump said in a statement, which was shared by one of his campaign advisers on Twitter.
The former president is known for his passion for golf, so it comes as no surprise he would want to offer a statement following the news of the crash.
The Los Angeles County Sheriff's Department confirmed Mr Woods was in a single-car crash early Tuesday morning near the Rolling Hills Estates and Rancho Palos Verdes neighbourhoods in Los Angeles, California. The professional golfer, 45, was extricated from his vehicle, according to the department, and Mr Woods was the only person involved in the crash.
Mr Woods' agent Mark Steinberg told Golf Digest that he suffered from "multiple leg injuries" and was undergoing surgery.
Olympic skier Lindsey Vonn, who dated Mr Woods for about three years before they split in 2015, said she was “praying” for her ex-boyfriend following the news.
“Praying for TW right now,” she wrote on Twitter.
Other celebrities and professional athletes have reacted to the golfer's car crash after news broke earlier on Tuesday.
"Prayers up for the GOAT @TigerWoods who was in an accident this morning," Jada Pinkett Smith tweeted. "Was just with him yesterday. Don't take not even a MOMENT for granted! I know you're good because your Tiger within is a beast!!!"
American golfer Justin Thomas said in an interview he was “sick to his stomach” following the news.
“It hurts to see ... now one of my closest friends get in an accident and man, I just hope he’s alright,” Mr Thomas said. “I’m just worried for his kids. I’m sure they’re struggling.” He also tweeted his reaction for his fans after the interview.
Other professional golfers have reacted to the news that one of their own was seriously injured, including Englishman Ian Poulter. “Thoughts are with @TigerWoods and others involved, wishing a speedy recovery and I hope the injuries are not bad,” he wrote on Twitter.
Justin Rose, an English professional golf star, wrote: “@tigerwoods, just seen the awful news. We know how tough you are, we’ve seen it a hundred times. Hoping and praying you’re ok my friend.”
Magic Johnson wrote on Twitter: “Everyone send your prayers out to Tiger Woods! He was just in a bad car accident. Let us all pray for his speedy recovery.”
NFL football player Reggie Bush said he was “praying” for Tiger Woods to “bounce back” following the crash.
Several organisations and brands have also reacted to the news of the professional golfer being hospitalised in Los Angeles.
PGA Tours said in a statement that they were “made aware” of the crash and were awaiting “further information” once Mr Woods comes out of surgery. “On behalf of the PGA Tour and our players, Tiger is in our prayers and will have our full support as he recovers,” the statement continued.
The Masters Chairman Fred Ridley said: “Tiger Woods is part of the Augusta National family, and the news of his accident is upsetting to all of us. We pray for him, for his full recovery and for his family during this difficult time.”
Nike, which has worked with Mr Woods since 1996, also issued a statement amid the news. “We are following the news around Tiger and our thoughts and heart are with him and his family at this time,” the brand said.
Professional footballers Gary Lineker and Gareth Bale also reacted to the news.
“Thoughts are with @TigerWoods. Hope it’s not as serious as appears,” Lineker wrote, while Bale said he was sending his “thoughts and prayers.”
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