The member for Edinburgh East said he can bring “a new perspective to our leadership team”.
Mr Sheppard joined the SNP in 2014 and was elected at the 2015 general election.
Declaring his intention to stand in a post on his website, he wrote: “We’ve had some great election successes recently, but frankly our opponents have made it easy for us.
“We need to prepare for the challenges ahead, including IndyRef2 when it comes. That will be a far tougher test, and we need to be ready.”
The deputy leader role became available after Stewart Hosie quit following newspaper disclosures about an affair.
The party’s Westminster leader Angus Robertson, MEP Alyn Smith and Inverclyde councillor Christopher McEleny are also in the running for the job.