The 24-year-old, who claimed 3000m bronze on Thursday, finished behind Ethiopia’s Genzebe Dibaba who claimed a double after also wining the 3,000m.
Muir was the third home star to win a medal during a frantic evening in Birmingham after hometown racer Elliot Giles claimed a surprise bronze in the men’s 800m and Eilidh Doyle clinched 400m bronze.
Muir said trackside: “I just got a taste of it after the 3,000. I just ran my socks off. I just thought ‘stay with them, be controlled’ and I came off with silver this time.”
Giles, who initially finished fourth, was upgraded to third after Drew Windle was disqualified for an apparent obstruction while Doyle - in the final after being upgraded in the semi-final following disqualifications - took her first individual world medal.
More than an hour after the 800m though Giles was still waiting for his medal to be rubber stamped after the American appealed.
However CJ Ujah had a bad day - he was disqualified from the 60m semi-final for a false start. The 23-year-old, part of the 4x100m world championship winning squad, was expected to challenge for the podium.
Muir, who finished in four minutes 06.23 seconds, overtook Sifan Hassan on the final lap after the Holland runner finished ahead of her in the 3,000m.
It represented a huge success for the Scot, whose only other major medals had come when she won double gold at the European Indoor Championships Belgrade last year
But in loaded fields in the 3000m and 1500m, against three-time 3,000m champion Dibaba, Sifan Hassan and Hellen Obiri Muir’s achievements need to be recognised.
Muir’s achievements, although not gold, top Katarina Johnson-Thompson’s pentathlon gold because of the strength of the respective fields.
She is now a serious competitor on the world stage and seems likely to improve, especially once she finishes her veterinary studies in May.
Muir will miss next month’s Commonwealth Games as she focuses on her final exams but will now be a marked woman at the European Championships in Berlin in August.
Co-captain Andrew Pozzi reached Sunday’s 60m hurdles final when he qualified fastest in 7.53 seconds - a season’s best - and he was joined by team-mate David King.
Earlier on Saturday, the men’s 4x400m relay squad reached Sunday’s final in 3:05.09, finishing behind the United States, having not run competitively with each other before. The women also made their final.
Also on Saturday morning, Jake Wightman and Chris O’Hara reached the men’s 1500m final and co-captain Shelayna Oskan-Clarke booked a place in the women’s 800m final.