It was mostly due to the influence of Abdul Karim, who initially entered her court as an attendant. Queen Victoria grew to like him, and promoted him to the rank of her personal clerk or secretary, and conferred many honors on him, including making him a commander of the Royal Victorian Order. It was under his influence that she began to learn Hindi/Urdu, and he was her teacher.

There was a great deal of friction in the Royal household over what was perceived as the Queen's favoritism towards Karim. For his part, Karim refused to be treated as a servant, which troubled both the other servants and aristocracy alike. On a few occasions when he traveled with Victoria to visit her many relatives, they would put him up in the servants' quarters and arrange his meals with the other servants. Karim objected, and Victoria took his part, often scolding her hosts for treating him like a servant. In her own home, Karim was treated very well.

By all accounts, there was a deep friendship between the two and they discussed all kinds of matters, including culture, philosophy, religion. As queen, Victoria had to remain somewhat aloof and dignified before her guests, but she had no such inhibitions with Karim, and often discussed personal details of her family and children with him, or any other concerns on her mind.

After Victoria died, Karim was kicked out of the palace and sent back to India. Her son, King Edward VII ordered that all correspondence between his mother and Karim be burned.

Her Hindi/Urdu speaking subjects thought nothing of it, because they didn't know. This was not a matter that British rulers wanted Indians to know, that the monarch was friendly with an Indian. Although the Court knew at the time, the world at large didn't become aware of the relationship until Frederick Ponsonby published his memoirs. Ponsonby was Equerry-in-Ordinary to Victoria and later Private Secretary to both King Edward VII and King George V. His memoirs describe Victoria's relation with Abdul Karim, and also the deep resentment in the Court against her perceived favoritism towards him.

If you're interested in reading more, there's a book called Indian Sahib: Queen Victoria's Dear Abdul by Sushila Anand. And an article in Vanity Fair about it. There's also a fictionalized "documentary" about it called Queen Victoria's Last Love, but it's not very historically accurate.

what was the reaction (if any) to this in Pakistan?

Just so you know, the Urdu language originated in the region that is now India, not in Pakistan. There are more native speakers of Urdu in India than in Pakistan, since people in Pakistan have different mothertongues (Punjabi in Punjab, Sindhi in the Sindh, Balochi in Balochistan, etc.), whereas Urdu is the first language for a huge number of people in India. Also, Abdul Karim was from Jhansi, which is a city in UP, pretty much in the center of what is now India.

Most Indians or Pakistanis who are aware of Abdul Karim would have learned of him in the 1950's, so that would be half a century after Victoria's death.