The 24-year-old had a recent spell on loan at Swindon Town, where he made 12 appearances.
He told Derby's official website: "We're pleased Chris has decided to join us and provide another option in attack.
"With Theo asking to go out on loan, there was obviously a need to bring in a replacement once a deal with Huddersfield was agreed. Initially, Chris is here for a month and we'll just take things from there."
Martin has made 117 appearances for Norwich, scoring 34 goals.