Most likely sometime after 25 BC, or even 23 BC. However, there is no concrete evidence; these dates are disputed and have been proposed by historians based on uncertain and / or circumstantial evidence.
Cicero Minor disappears from the known historical record after his appointment to the legateship of Syria (then comprising approximately modern-day Syria, Lebanon and Israel) from 28 or 27 BC and the proconsulship of Asia either before or - more likely - after his stint in Syria. English Wikipedia's List of Roman governors of Syria gives the dates of Cicero Minor's governorship as 28 to 25 BC but does not provide sources; the List of Roman governors of Asia either includes or excludes him depending on the language (e.g. the English page excludes him, the Latin page includes him). What follows aims to provide some evidence on the dates.
As Cicero Minor was suffect consul for 30 BC and as the legateship of Syria was held by Marcus Valerius Messalla Corvinus in 29 BC, the posting to Syria would not have been until 28 BC at the earliest (which was when Corvinus was sent to Gaul, thereby creating a vacancy). The collective historical work Prosopographia Imperii Romani cites (in Part 3) Appian as the source for Cicero Minor's appointment. This source is cited by G. W. Bowersock, 'Augustus and the Greek world', Chapter 2 'Roman Magistrates in the Augustan East'. Appian provides the most details of Cicero Minor's career under Augustus:
Octavian, by way of apology for his betrayal of Cicero [Minor], caused him to
be appointed pontifex, and not long afterwards consul and then
proconsul of Syria. When the news of the overthrow of Antony at Actium
was forwarded by Octavian this same Cicero, as consul, announced it to
the people and affixed it to the rostra where formerly his father's
head had been exhibited.
It seems that Cicero Minor no longer held the position(s) in Syria by 25 BC (and possibly as early as 27 BC) as there is possible evidence from coins naming Marcus Terentius Varro as governor by 25 BC. However, the dating is not certain and this does not rule out the possibility that Varro was appointed in 27 or 26 BC. Cicero Minor may have lost the position following Augustus's reorganization in 27 BC but, again, there is no evidence for this. The governorship of Asia has also been proposed for Cicero Minor for the year 24 / 23 BC, this based on circumstantial evidence (an anecdote in Seneca relating to the rhetorician Lucius Cestius Pius). An alternative, less well-supported, view is that he was governor for Asia in 29 / 28 BC. However, the latter seems unlikely given the usual 5 or 6 year gap at the time between consul and proconsul (in Cicero's case, 30 BC for the former so 25 or 24 BC for the latter).
Cicero Minor appears to have been not without administrative and military ability despite an apparent weakness for alcohol. Pardoned by Octavian for siding with Brutus and Cassius at the Battle of Philippi (42 BC), the younger Cicero fought against Mark Anthony Actium (31 BC). Maurice Testard, in 'Le fils de Cicéron, destinataire du De Officis' (Bulletin de l'Association Guillaume Budé, n°2, juin 1962) is one of several sources (perhaps citing Appian) which suggest that Augustus may have offered young Cicero his various positions because, as Octavian, he had agreed to the elder Cicero being proscribed by Mark Anthony (and subsequently killed).
Conflicting information, and wrongly-sourced or unsourced statements in Wikipedia
French Wikipedia on Cicero Minor gives 28 to 25 BC as the dates for his time in Syria; however, none of the many primary sources cited actually state this (in fact, most of them only mention his role as consul in 30 BC). Several pages in other languages seem to have copied the French. The Italian Wikipedia page implies that he died in Syria in 27 BC but gives no source. German Wikipedia is at first (wisely) more circumspect on Syria, stating "probably" 27 - 25 BC, but then gives an unsourced date of 23 BC for proconsul of Asia.