The 28-year-old, who won the 1500m at the World Championships last month, finished behind Australia’s Oliver Hoare and Kenya’s Timothy Cheruiyot in three minutes 30.53 seconds.
Scotland’s Wightman was hoping to win three gold medals this summer and must now focus on the 800m at the European Championships later this month.
After Wightman’s stunning victory at the worlds a little over two weeks ago in Eugene, a capacity crowd packed into a sun-kissed Alexander Stadium with hopes of watching the Scotsman do it again.
But the roars were not enough to lift Wightman to the top of the podium as Hoare timed his move to perfection down the home stretch, coming from fourth to pip Cheruiyot at the line.
Hoare finished in a Games record time of three minutes, 30.12 seconds with Cheruiyot just 0.09 seconds back to take silver and Wightman settling for bronze.