The Spaniard was downed in the Hamburg European Open final by Lorenzo Musetti over the weekend but nevertheless saw a rise in his stature to a career-high position of fifth.
In doing so, it makes the 19 year-old the second-youngest male to break into the top five this century, trailing only Nadal and bettering Novak Djokovic by a matter of months.
"It means a lot," Alcaraz said. "The hard work that I put in every day for reaching my dreams, [number] 1, and little by little I'm reaching my dream.
"Top five for me is pretty amazing and I will keep going to be [number] 1."
Had Alcaraz won in Hamburg, he would have risen to fourth, while other movements in the rankings include a rise to number 31 for Musetti and a return to the top 200 for Dominic Thiem, at number 199.