Sinner wore a protective sleeve on his right arm and could be seen grimacing at times in his 7-6 (2), 6-4, 6-4 quarter-final victory against 10th seed Shelton on Court One, but the 23-year-old battled through the discomfort.
Sinner had sparked fears he may have to pull out of Wimbledon after injuring his right elbow in an awkward fall during his fourth-round tie against Grigor Dimitrov on Monday. The Italian top seed was trailing by two sets and on the brink of a shock defeat when Dimitrov pulled a pectoral muscle while serving and had to retire from the match.
Sinner, a three-time Grand Slam champion, cancelled a scheduled practice session at the All England Club on Tuesday and had an MRI scan on his injury.
The top seed, who has never made the Wimbledon final, is the first Italian man to reach the last four at the All England Club multiple times, following his previous semi-final appearance in 2023.
Beaten by Carlos Alcaraz in an epic French Open final in June, when he blew a two-set lead and squandered three championship points, Sinner had been revitalised in his first three matches at Wimbledon. He dropped just 17 games to equal a 53-year-old record for the fewest games conceded en route to the Wimbledon men's last 16.
But his injury had thrown into doubt his bid to reach a fourth successive Grand Slam final.
However, while Shelton had surpassed dad and coach Bryan, who reached the Wimbledon last-16 31 years ago, he was no match for Sinner, even if the Italian was not 100 per cent fit.
Sinner ground his way through a gruelling first set lasting 52 minutes.
He looked more uncomfortable as the match wore on, with a concerned expression on his face after grabbing his elbow following a big groundstroke in the sixth game of the second set.
However, Shelton was also in the wars and the 22-year-old needed his left ankle re-taped late in the set.
Sinner broke in the 10th game to move into a two-set lead.
The third set was a tight affair, going with serve until the 10th game, when Shelton faltered.
Sinner needed three match points but celebrated when the American went long.