Does any scripture predict the Muslim invasion of India?
Does the scripture like the Bhavishya Purana or some other Purana predict an invasion?
Does the Bhagavata Purana predict the Muslim invasion of India?
It may. The Muslim invasion of India, and the subsequent conquest of northwest India into the formation of what is now Pakistan, may have been predicted by the Rishis in the Bhagavatam.
CHAPTER ONE: The Degraded Dynasties of Kali-yuga
Text 37: The land along the Sindhu River [modern day Pakistan], as well as the districts of Candrabhāgā, Kauntī and Kāśmīra [modern day Pakistan and Afghanistan], will be ruled by śūdras, fallen brāhmaṇas and Mlecchas. Having given up the path of Vedic civilization, they will have lost all spiritual strength.
Text 38: There will be many such uncivilized kings ruling at the same time, O King Parīkṣit, and they will all be uncharitable, possessed of fierce tempers, and great devotees of irreligion and falsity.
Texts 39-40: These Mlecchas in the guise of kings will devour the citizenry, murdering innocent women, children, cows and brāhmaṇas and coveting the wives and property of other men. They will be erratic in their moods, have little sattva guna and be very short-lived. Indeed, not purified by any Vedic rituals [samskaras] and lacking in the practice of regulative principles [nitya karmas], they will be completely covered by the modes of passion [rajas] and ignorance [tamas].
Text 41: The citizens governed by these low-class kings will imitate the character, behavior and speech of their rulers. Harassed by their leaders and by each other, they will all suffer ruination.
CHAPTER TWO: The Symptoms of Kali-yuga
Text 7: As the earth thus becomes crowded with a corrupt population, whoever among any of the social classes shows himself to be the strongest will gain political power.
Text 8: Losing their wives and properties to such avaricious and merciless rulers [Mlecchas], who will behave no better than ordinary thieves, the citizens will flee to the mountains and forests.
Text 9: Harassed by famine and excessive taxes, people will resort to eating leaves, roots, flesh, wild honey, fruits, flowers and seeds. Struck by drought, they will become completely ruined.
Text 10: The citizens will suffer greatly from cold, wind, heat, rain and snow. They will be further tormented by quarrels, hunger, thirst, disease and severe anxiety.
However, the above reference to Mlecchas might not even be referring to Muslims; it could be referring to much more ancient invaders, like the Greeks, Yavanas, Huns, Scythians, Persians, etc.
Darius, the Persian emperor, invaded and conquered the Indus Valley.