Madonna, 38, watched her friend Sian Phillips play the Hollywood star in the Lyric Theatre's production of Marlene and afterwards went backstage to chat to the Welsh-born veteran.
The singer arrived in Britain last Thursday and is house-hunting and writing songs. But she was determined to keep a low profile at the theatre and did not even visit the VIP suite during the interval. A staff member said: "She wore a black top and was very dressed down. She certainly did not want to draw any attention to herself.
"She sat in her seat during the interval and looked quite relaxed and happy. Afterwards she went backstage with Shirley Bassey and spoke to Sian."
Marlene is set in a theatre in Paris during the Seventies and follows Dietrich's world tour, which began in 1953. Dietrich died in 1992 and was known to have followed a bisexual lifestyle.
Phillips was last seen performing in London as Madam Armfeldt in A Little Night Music which was also watched by Madonna at the National Theatre.
Madonna was accompanied by her baby, Lourdes, and is believed to want her to be educated in Britain.