I think the concept of "distributed systems" is very broad.
Do you mean service oriented architectures? That's the practical 'distributed' systems many companies are using today. You don't need a degree- just go work at Amazon for a couple years.
Do you mean decentralized systems and algorithms? Paxos, Raft, Bitcoin and TOR? Then sure, you might consider a master's degree. Or just start reading papers online and messing around with code in your spare time.
Do you mean service oriented architectures? That's the practical 'distributed' systems many companies are using today. You don't need a degree- just go work at Amazon for a couple years.
Do you mean decentralized systems and algorithms? Paxos, Raft, Bitcoin and TOR? Then sure, you might consider a master's degree. Or just start reading papers online and messing around with code in your spare time.