He holds National Series records for hits (152) and doubles (35) in a season (1999, 90 games), and was part of Cuba's gold medal-winning team at the 2004 Summer Olympics and the second place team at the 2006 World Baseball Classic.
He has one brother and one sister.
Enríquez was left off of Cuba's roster for the 2000 Olympics, with some speculating fear of defection and others opining that it was due to Michel's youth (still just 21 years old) and lack of experience in international tournaments relative to some of the other available options. He hit .353/.451/.595 in the 2000-2001 Serie Nacional.