He was the son of the Prussian captain a. D. Christian Ludwig von Glümer (born 1772) and his wife Wilhelmine, née Spohr.

Between 1847 and 1851 he was adjutant of the 7th Landwehr Brigade, participated in the 1849 campaign against the insurgents in Baden, in 1856 became a Major in the staff of the 11th Division and in 1858 he was transferred to the VI.

In 1859 Glümer became the commander of the Fusilier Battalion in the 23rd Infantry Regiment in Neisse, then director of the division school there and soon afterwards a lieutenant colonel.

In addition, he received the Military Karl-Friedrich Merit Order and, on 5 February 1871, the prestigious Pour le Mérite.

After the peace he was appointed commander of the 29th Division in Freiburg im Breisgau, and on 8 March 1873, Glümer became governor of the Metz fortress.