Is Hunting in the Sacred Months Prohibited?
Question

Is hunting in the Sacred months prohibited?
Praise be to Allah.What are the sacred months? 
The sacred months are Rajab, Dhul Qa`dah, Dhul Hijjah and Muharram . These are what are referred to in the verse (interpretation of the meaning): 
“Verily, the number of months with Allah is twelve months (in a year), so was it ordained by Allah on the Day when He created the heavens and the earth; of them four are Sacred (i.e. the 1st, the 7th, the 11th and the 12th months of the Islamic calendar). That is the right religion, so wrong not yourselves therein.” [At-Tawbah 9:36]
Is hunting in the sacred months prohibited?
There is nothing wrong with hunting in the sacred months ; rather the prohibition on hunting is connected to two things: 

Ihram for Hajj or `Umrah, because Allah says (interpretation of the meaning): 

“O you who believe! Kill not the game while you are in a state of Ihram [for Hajj or `Umrah (pilgrimage)], and whosoever of you kills it intentionally, the penalty is an offering, brought to the Ka`bah, of an eatable animal (i.e. sheep, goat, cow) equivalent to the one he killed, as adjudged by two just men among you; or, for expiation, he should feed poor persons, or its equivalent in fasting, that he may taste the heaviness (punishment) of his deed. Allah has forgiven what is past, but whosoever commits it again, Allah will take retribution from him. And Allah is All-Mighty, All-Able of Retribution.” [Al-Ma’idah 5:95]
Ibn Kathir (may Allah have mercy on him) said:  
“This is Allah’s prohibition on killing game when in the state of Ihram , and a prohibition on being involved in any activities of this nature. " (Tafsir Ibn Kathir  2/99)

Hunting within the limits of the Sanctuary, which means Makkah and Madinah, because of the Hadiths that were narrated concerning that. 

It was narrated from Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) stood up on the day of the Conquest and said:
“Allah sanctified Makkah the day He created the heavens and the earth, so it is sacred by the sanctity decreed by Allah until the Day of Resurrection. It was not permitted for anyone before me to fight therein and will never be permitted to anyone after me, and it was only permitted to me for part of a day. Its game is not to be disturbed and its thorns are not to be cut.” (Narrated by Al-Bukhari, 1284 and Muslim, 1353). 
The relevant point here is the words of the Prophet (peace and blessings of Allah be upon him), “Its game is not to be disturbed.” This hadith clearly states that it is prohibited to disturb the game of Makkah, so it is more appropriate that hunting itself is forbidden. 
As for Madinah, it is proven in an authentic Hadith that Abu Hurayrah (may Allah be pleased with him) used to say: If I saw gazelles grazing in Madinah I would not disturb them. The Messenger of Allah (peace and blessings of Allah be upon him) said: “The area between its two lava fields is a sanctuary.” (Narrated by Al-Bukhari, 1774 and Muslim, 1372) 
The lava fields are the harrahs or areas of black stone, and Madinah is between two lava fields, east and west.  
As for the sacred months, there is no connection between them and the prohibition on hunting. 
And Allah knows best.