LATIN DICTIONARYLexicon Latīnum
nounfirst declension

missa prīvāta

missa prīvāta f (genitive missae prīvātae)
Ecclesiastical[ˈmis.sa priˈvaː.ta]

Meaning

  1. EcclesiasticalLatinLow Mass (Mass that is not sung)
    Si vero ob aliquam causam Missa in cantu non celebratur, Missa privata SS. Sacramenti legi poterit in iis diebus in quibus per rubricas licet, nempe quocumque die officium non est duplex, aut de Dominica, aut dies in qua prohibetur fieri de festo duplici.But if for some reason a sung Mass is not celebrated, a Low Mass of the Holy Sacrament may be read on those days on which it is licit according to the rubrics, whenever, of course, the office of the day is not a double, or that of a Sunday, or a day on which it is prohibited to be of a double feast.1883, “Ordo Servandus in Oratione Quadraginta Horarum, in Dioecesi Baltimorensi”, in The Pastor, volume 1, number 9, page 212:
  2. EcclesiasticalLatinprivate Mass (Mass with no congregation present or communicating)

Declension

declension
formsingularplural
nominativemissa prīvātamissae prīvātae
genitivemissae prīvātaemissārum prīvātārum
dativemissae prīvātaemissīs prīvātīs
accusativemissam prīvātammissās prīvātās
ablativemissā prīvātāmissīs prīvātīs
vocativemissa prīvātamissae prīvātae

Origins

“Low Mass” is the original sense, from prīvātus, “deprived”. The sense “private Mass” is probably from conflation with later cognates of prīvātus, e.g. English private, French privé.

Quick answers

What does missa prīvāta mean in Latin?
missa prīvāta, a noun, means “Low Mass (Mass that is not sung); private Mass (Mass with no congregation present or communicating)”.
What is the genitive of missa prīvāta?
The genitive singular is missae prīvātae. missa prīvāta is first declension.