The movie leapt well beyond the expectations of industry analysts, who had figured the movie would debut in the $25 million range.
"Hop" matched the year's best debut for "Rango," which opened a month ago with $38.1 million.
The film follows a runaway bunny, voiced by Brand, who finds refuge with a grown-up slacker, played by James Marsden.
Jake Gyllenhaal's thriller "Source Code" debuted at No. 2 with $15.1 million, and the haunted-house flick "Insidious" opened at No. 3 with $13.5 million.
Last weekend's top movie, "Diary of a Wimpy Kid: Rodrick Rules," fell to No. 4 with $10.2 million, raising its total to $38.4 million.
1. "Hop," $38.1 million.
2. "Source Code," $15.1 million.
3. "Insidious," $13.5 million.
4. "Diary of a Wimpy Kid: Rodrick Rules," $10.2 million.
5. "Limitless," $9.4 million.
6. "The Lincoln Lawyer," $7.1 million.
7. "Sucker Punch," $6.1 million.
8. "Rango," $4.6 million.
9. "Paul," $4.3 million.
10. "Battle: Los Angeles," $3.5 million.
The Associated Press contributed to this report.