Yes the duration of Christ’s ministry was prophesied under the Old Testament to be 3.5 years
25 “Know and understand this: From the time the word goes out to restore and rebuild Jerusalem until the Anointed One, g the ruler, comes, there will be seven ‘sevens,’ and sixty-two ‘sevens.’ It will be rebuilt with streets and a trench, but in times of trouble. 26 After the sixty-two ‘sevens,’ the Anointed One will be put to death and will have nothing. The people of the ruler who will come will destroy the city and the sanctuary. The end will come like a flood: War will continue until the end, and desolations have been decreed. 27 He will confirm a covenant with many for one ‘seven.’ In the middle of the ‘seven’ he will put an end to sacrifice and offering. And at the temple he will set up an abomination that causes desolation, until the end that is decreed is poured out on him.” (Daniel 9:25–27, NIV).
This question is related to this post: Does the Old Testament foretell the time in history in which the Messiah would come (the first time)?
There are many possible interpretations according to the seventy weeks of Daniel followed by one half of a week where Messiah would be ‘cut off. I prefer the view that each day of the weeks are 1 year and the basic idea is this:
The period is 490 years ending 3½ years after Christ’s death. The 490 years begin with the decree by Artaxerxes I. (Ezra 7) The appearance of Messiah at the end of the 483 years is when Christ is baptized. This is where his ministry begins at which point ½ a week later (3.5 years) he is ‘cut off’ through his crucifixion. Therefore Christ put an end to sacrifice and offering as the inner curtain of the temple as torn top-to-bottom. Through the Holy Spirit for another 3½ years after His crucifixion Christ offers salvation principally to the Jews but having generally rejected him thereby sealing the cause of the future destruction of Jerusalem [abomination of desolation], which occurred several years later. This final destruction of Jerusalem as a result is also a final ending of the sacrifices and offering but the true end was in Christ's death, the second part of it is more penal and judiciary against those who rejected him.
There are many variants and debates about the exact years, some even think the 3.5 years is the last of the ½ week. However in either case it does seem that Jesus came around the time he should have and his ministry lasted for around the 3.5 years that it should have. Regardless of the view you take it is compelling and believable.