There are a lot of Qur'anic Ayahs and Prophetic Hadiths to this effect. Some Muslim scholars have denied and warned against celebrating the Prophet's Mawlid, depending on some religious evidence like those mentioned above and others. However, some contemporary scholars consider such a celebration permissible as long as no violations are committed.
O you who believe! Obey Allâh and obey the Messenger (Muhammad ﺻﻠﻰ ﺍﷲ ﻋﻠﻴﻪ ﺳﻠﻢ), and those of you (Muslims) who are in authority. (And) if you differ in anything amongst yourselves, refer it to Allâh and His Messenger (ﺻﻠﻰ ﺍﷲ ﻋﻠﻴﻪ ﻭﺳﻠﻢ), if you believe in Allâh and in the Last Day. That is better and more suitable for final determination.
On referring such a question of celebrating the Prophet's Mawlid to the Holy Book, we find that it orders us to follow all that the Prophet (peace be upon him) enjoins and to avoid all that the Prophet forbids.
And they say, "None shall enter Paradise unless he be a Jew or a Christian." These are their own desires. Say (O Muhammad ﺻﻠﻰ ﺍﷲ ﻋﻠﻴﻪ ﻭﺳﻠﻢ), "Produce your proof if you are truthful."
Do not exceed the limits in your religion for those who preceded you have been destroyed due to their excessiveness in religion.
Do not extol me as the Christians extolled Mary's Son (i.e., Jesus Christ), as I am a servant, so it is better for you to say, "Allah's Servant and Messenger."
After that, surely, you will die. Then (again), surely, you will be resurrected on the Day of Resurrection.
I will be the first to rise from my grave on the Day of Resurrection and I will be the first intercessor and the first whose intercession will be accepted (by Allah).
Allâh sends His Salât (Graces, Honours, Blessings, Mercy) on the Prophet (Muhammad ﺻﻠﻰ ﺍﷲ ﻋﻠﻴﻪ ﻭﺳﻠﻢ), and also His angels (ask Allâh to bless and forgive him).
O you who believe! Send your Salât on (ask Allâh to bless) him (Muhammad ﺻﻠﻰ ﺍﷲ ﻋﻠﻴﻪ ﻭﺳﻠﻢ), and (you should) greet (salute) him with the Islâmic way of greeting (salutation i.e. AsSalâmu 'Alaikum ).
Also, the Prophet (peace be upon him) said: If anyone invokes blessings on me once, Allah will bless him ten times.
Sending peace and blessings on the Prophet is desirable at all times, stressed at the end of each Salah (Prayer), and even obligatory by some scholars in the second half of Tashahhud (a recitation in the sitting position in the second/ last unit of Prayer). Besides, it is a Stressed Sunnah in many situations, such as the time after Adhan (call to prayer), the time after hearing the name of the Prophet (peace be upon him), and on Friday during the day and night, as reported in many Prophetic Hadiths.
It is Allah Who can guide us and all Muslims to be knowledgeable and steadfast adherents of His religion, to lead all Muslims to adhere steadfastly to the Prophetic Sunnah and to avoid all forms of Bid`ah. Allah is the Most Generous and the Most Beneficent! May Allah's Peace and Blessings be upon our Prophet Muhammad, his family and Companions!