Merkel announced her decision on Friday after Erdogan demanded that Germany press charges against Jan Boehmermann after he recited a sexually crude satirical poem about the Turkish leader on German public broadcaster ZDF on March 31.
A section of the German criminal code prohibits insults against foreign leaders but leaves it to the government to decide whether to authorize prosecutors to pursue such cases.
This put Merkel in an awkward position as she has been the driving force behind a European Union deal with Turkey to stem the flow of refugees into Europe.
Sunday's survey by pollster Emnid for the Bild am Sonntag newspaper found that 66 percent of those questioned opposed Merkel's decision to allow prosecutors to pursue the case. Only 22 percent said she was right, with 12 percent undecided.
Emnid polled 500 people on Friday afternoon.
Merkel's decision had already divided her ruling coalition and prompted accusations that she failed to protect free speech.