Yeah, University of Notre Dame does provide scholarships based on merit. Here are some of them:

Besio Family Scholarship
Total Worth: $25,000 per year
Eligibility: $25,000 per year
Minimum Criteria: Based on outstanding academic achievement, character, and community service.

University of Notre Dame provides aids at an average of 47455 per student meeting 100% of students need. 100% of students with need receive financial aid at an average of 38673 need-based grant. They also provide other scholarships including Brennan Family Scholars Program and Edward W. Devine Scholarship.