He was one of the sons and among the children born to Marcus Licinius Crassus Frugi (consul 64) with his wife Sulpicia Praetextata, daughter of the suffect consul in 46, Quintus Sulpicius Camerinus Peticus and a grandson of Marcus Licinius Crassus Frugi, who had been consul in 27 and Scribonia. His brother Gaius Calpurnius Piso Crassus Frugi Licinianus had been a consul in 87. The father of Frugi was executed by the emperor Nero between 66 and 68, because of information brought against him by Marcus Aquilius Regulus. After the death of his father, his mother took him with his siblings, to a Senate meeting in 70 early in the reign of Vespasian, seeking vengeance for his father’s death. Regulus and his associates were prosecuted by the Senate.
According to the Augustan History, Frugi was of consular rank and refers to him as a former consul. Frugi served as a suffect consul in 88. Pliny the Younger reports him speaking aggressively in the Senate in 101.
It has been argued that Frugi married the niece of the emperor Trajan, Salonina Matidia, as her third husband. If so, Frugi and Matidia had a daughter called Rupilia Faustina. In any case, Rupilia Faustina became the paternal grandmother of Marcus Aurelius.
Except where otherwise noted, the notes below indicate that an individual's parentage is as shown in the above family tree.