The public prosecutor's office in Mainz, western Germany, said Erdogan had formally filed a request to have the decision overturned.
The suit was filed by Erdogan's lawyer on Sunday, Mainz head prosecutor Andrea Keller said in a statement.
The appeal will be handled by the general prosecutor's office in Coblenz, she said.
The episode has had a toxic effect on German-Turkish relations, casting a shadow over attempts to stem the influx of Syrian migrants via Turkey.
Boehmermann recited a so-called "Defamatory Poem" satirically accusing of Erdogan of bestiality and paedophilia.
Boehmermann said the piece was a reaction to Ankara's decision to summon Germany's ambassador over another satirical song broadcast on German TV which lampooned Erdogan in far tamer language.
The comic acknowledged the poem was intended to provoke, and would flout Germany's legal limits to free speech.
But the poem did not go down well in Ankara and Erdogan filed a criminal complaint.
In April, Chancellor Angela Merkel authorised an investigation as to whether Boehmermann could be convicted under rarely-enforced 19th-century laws on lese majeste -- a decision that earned her a rebuke from German rights groups.
"There is no evidence that the accused was making a serious attack on the personal or social reputation of the Turkish president," they concluded.
German prosecutors are scheduled to rule next month on another aspect of Erdogan's complaint, which calls for a ban on all further broadcasts of the poem.
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