Muir clocked four minutes 06.23 seconds, behind Dibaba (4:05.27), with Netherlands' Sifan Hassan third.
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.
Hassan trains as a member of the Nike Oregon Project.
American Paul Chelimo, a world 5,000m silver medallist, faces a hugely strong young Ethiopian contingent in the men's 3000m in 18-year-old Selemon Barega, victor of the world under-20 5,000m title in 2016 and the world under-18 3,000m title last year, Hagos Gebrhiwet, the 23-year-old Olympic 5,000m bronze medallist, and defending champion Yomif Kejelcha, who earned a wild card for the championships by winning the IAAF World Indoor Tour.
US champion Shelby Houlihan, who trains with the Portland-based Bowerman Track Club, closed hard to take fifth in 8:50.38.
In total, six athletes across five events at three previous editions of the IAAF World Indoor Championships, have accepted invitations to receive their reallocated medals in Birmingham. "Tomorrow in the 1500m I will try to get gold medal number two".
She undertook a six-hour taxi journey to get to Birmingham on Wednesday as Britain's roads felt the impact of the freezing temperatures and heavy snow. "I just tried my best to the end of the competition".
Naide Gomes (POR), who was promoted to silver in the long jump in 2006, Li Meiju (CHN) and Misleydis Gonzalez (CUB), who were promoted to silver and bronze in the shot put in 2008 and Olga Rypakova (KAZ), promoted to bronze in the triple jump for 2008, are unable to attend.
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Griffin said he hopes he's an inspiration to kids everywhere. "I'm planning on doing both linebacker and DB drills", Griffin said. He's a jack-of-all-trades defensive player from the University of Central Florida , who became a late invite to the NFL Combine.
Her team-mate Eilish McColgan came 10th in the 3,000m.
Doyle battled Wimbley for the inside track space with 200 metres to go and took up a strong position, only for Wimbley to hunt her down in the home straight with Okolo in a class of her own.
It was a slow pace race that saw Briton, cheered by home crowed take the lead as the pack went through the 400m in 1:15 while defending champion Dibaba was cruising at the back of the bunched group. "It's not my preferred event so to do this is really incredible".
Barshim added: "I'm happy with the medal but not quite the result". Britain's CJ Ujah was expected to challenge for a medal but blew it with a false start in his semi-final.
"Being so close to silver [in the 3,000m], after that race I knew I was in similar shape to Hassan and I could get the silver and beat her".
Eighteen-year-old Castletroy College student Neville has a personal best of 7.30 seconds for the 60m indoors, while her season's best time is 7.34.
Part of the men's 4x100m world title-winning squad last summer Ujah opted to miss the Commonwealth Games to focus on his indoor goals. The little mistakes he made he can resolve with a drill session in his warm-up.