The 20-year-old Cardiff Blues wing made his Lions debut in the win over the Free State Cheetahs last weekend and was due to be on the replacements bench tonight for the game against The Sharks.
But he aggravated his thigh problem in training this week and was sent to hospital for a scan on Tuesday.
"Leigh unfortunately hurt his right thigh muscle during Monday afternoon's training. Following a medical assessment it was decided that he should undergo a scan to determine the extent of the injury," explained Lions head coach Ian McGeechan.
"He had the scan on Tuesday morning and that confirmed a presence of a further muscle injury to his right thigh which will require three to four weeks of rehabilitation. That means he will miss the rest of the tour.
"I'm especially disappointed for Leigh as he worked so hard to come back from the set-back at the start of the tour but he has proven his strength of character by the way that he is handling the news and we wish him a quick recovery.
"Leigh will travel with us to Cape Town and then return to the UK to continue his rehabilitation with the Cardiff Blues. We will not be replacing Leigh as we have enough cover for his position amongst the group of players that we have."
Lions tour manager Gerald Davies added his view on the latest injury blow: "We are obviously very disappointed that Leigh has sustained a further injury and we understand that this must be particularly frustrating that this has happened a second time, especially for a young man embarking on his rugby career but we wish him well for his rehabilitation."