Meinrad was a son of Prince Maximilian I of Hohenzollern-Sigmaringen (1636–1689) from his marriage to Maria Clara (1635–1715), the daughter of Count Albert of Berg-s'-Heerenberg.
He was still a minor when he succeeded his father in 1689 and initially, he stood under the guardianship of his mother and his uncle Franz Anton, Count of Hohenzollern-Haigerloch.
In 1692, Emperor Leopold I raised the Swabian branch of the House of Hohenzollern to Imperial Princes, under the condition that they would practice primogeniture in the future, i.e. they were not allowed to increase the number of imperial princes by further subdividing their principalities.
Both his sons had joined the clergy, so Hohenzollern-Haigerloch fell back to Hohenzollern-Sigmaringen.
On 22 November 1700 in Sigmaringen, he married Johanna Katharina von Montfort, (1678–1759), a daughter of Count John Anthony I of Montfort-Tettnang.