The Roman satirists were Ennius, Lucilius, Horace, Persius, Juvenal, Varro, Seneca, and Petronius. First century A.D. satirists Seneca and Petronius are credited with writing the Menippean Satires Apocolocyntosis and the novelistic Satyricon. Varro (b. 116 B.C.) also wrote Menippean Satire, but although St. Jerome catalogued 150 books of Varro's Saturae Mennipeae, only short fragments remain.
In "On the Origin of "Menippean Satire" as the Name of a Literary Genre," Joel C. Relihan (Classical Philology, Vol. 79, No. 3 (Jul., 1984), pp. 226-229) says that Menippean satire was not considered a separate genre of satire by the Romans, but simply a variation on the model of satire used by Ennius. He says there is no ancient Roman mention of the sub-genre of Menippean satire. Only Varro's 150 pieces make use of the name Menippus.
For more on satire, read Roman Satire by Michael Coffey.