An injunction is equitable relief. The general rule is 'no right to jury for claims solely seeking equitable relief.' It may vary by jurisdiction.
History: equitable relief can only be granted when there is inadequate relief at law. Originally only Chancellors could issue such relief. Today, most (but not all) states have integrated the courts of chancery into the law courts. However, there was no right to jury in courts of chancery (the chancellor decided the facts, the law, and the remedy, all without a jury), and that non-right has followed the equitable claims into law courts.