Meinecke was born in Vienna but grew up in Istanbul after his father accepted a position as director and stage designer at the City Theatre.
[1] After graduation he joined the German Archaeological Institute in Cairo in 1969 and devoted himself to preserving architecturally and historically significant buildings in the old town, especially those from the Mamluk period.
[1] One result of this work was the extensive study that formed his professorial thesis in 1978: Mamluk architecture in Egypt and Syria.
[1] This preservation work included a 1980 collaboration on restoration of the 10th-century Fatimid Darb Qirmiz Quarter in Cairo, for which he was among the recipients of the 1983 Aga Khan Award for Architecture.
After Meinecke's death, his position as director was filled by Volkmar Enderlein, the longtime head of the Islamic collection of Museum Island.