MEXICO CITY—From Mexico to Brazil, most Latin American governments have remained impassive as the Venezuelan government violently cracks down on growing protests, arrests opposition leaders and censors most of the country's media.

Ideological affinity with Venezuela's leftist government and economic interests, including the country's oil largess, have complicated the response—or lack thereof—in the region. "The silence has been deafening," said Michael Shifter, the president of the Washington-based think tank, the...