The Scot, 23, beat Russian Liliya Shobukhova's record by 1.45 seconds to post a new mark of eight minutes 26.41 seconds, fifth on the world-best list.
Muir is preparing for next month's European Indoor Championships.
England's Andrew Pozzi won the 60m hurdles in Germany in 7.44 seconds - the fastest time in the world this year and-third fastest in British history.
Pozzi ran a personal best of 7.49 in the heats before bettering that mark as he finished 0.14secs outside Colin Jackson's British record in the final.
Dina Asher-Smith set a world best time of 7.13 in the 60m heats before being edged into second in the final by Jamaican Gayon Evans (7.14).
Muir broke the British indoor 5,000m indoor record in Glasgow last month, and took Kelly Holmes' British 1500m record outdoors last July.
She then beat her own 1500m mark in Paris on her way to winning last year's Diamond League title.
As well as the European Indoor Championships in Belgrade in early March, she is also targeting a medal at the World Championships in London in August, after finishing seventh in last year's 1500m Olympic final in Rio.
Media playback is not supported on this device

The Football Association's independent regulatory commission partially upheld an appeal lodged by Chelsea on Tuesday.
Matic, 26, was sent off in Saturday's 1-1 draw with Burnley after reacting to a high tackle from Ashley Barnes.
In a statement, Chelsea said they were "extremely disappointed and frustrated" that Matic must still serve a ban.
Matic will miss the League Cup final against Tottenham Hotspur at Wembley and next week's league match at West Ham United, on Wednesday 4 March.
A statement on Chelsea's website, published under the headline 'Chelsea FC appalled with the FA's decision on Matic', said the board was unhappy that the commission decided against reducing the ban by the "maximum extent permitted under FA rules".
The commission could have reduced the ban to one game, but could not overturn the red card.
The Chelsea statement added: "There has been universal condemnation of the reckless challenge made by Ashley Barnes on Matic and it is the club's view that he has been unjustly punished with a two-match ban for his reaction to a career-threatening tackle."
The Serbia midfielder pushed Barnes to the ground after the Clarets forward caught him on the shin.
Blues boss Jose Mourinho defended Matic's reaction and described the tackle from Barnes as "criminal", while Match of the Day pundit Alan Shearer said the challenge was "horrific" and "dangerous".
However, Burnley manager Sean Dyche said that while slow-motion replays made the incident look "ugly", the challenge was merely a "coming together at an unusual angle".
Roger Burden, chairman of the FA's regulatory commission, said the panel had "rejected the mitigation advanced by Nemanja Matic in respect of the provocation and tackle he received which led to his act of violent conduct".
He added: "The violent response of Mr Matic to the nature of the tackle cannot be condoned and does not vindicate his subsequent actions.
"The members of the commission did, however, accept the mitigation in respect of the level of force used by Mr Matic and the nature of the contact he made with Mr Barnes."
Chelsea's statement added that they would await the FA's written reasons before commenting further, and said "referees and the football authorities must do more to protect players at all levels of the game from dangerous challenges".

Richard Hilary, 66, is accused of committing 15 offences while he was a teacher at the Wavell School in Farnborough.
The alleged victims were under the age of 16 at the time.
Mr Hilary, of Northend Lane, Droxford, has been bailed to appear before Basingstoke magistrates on 2 May.
Laura Muir continued her recent record-breaking form by setting a European 3,000m indoor record in Karlsruhe.
[NEXT_CONCEPT]
Chelsea midfielder Nemanja Matic's violent conduct ban has been reduced from three games to two, but he will still miss Sunday's League Cup final.
[NEXT_CONCEPT]
A man has been charged with sexually attacking girls while he worked at a secondary school in Hampshire in the late 1970s and early 1980s.