No you don’t have to get an MCP or MCSE before attempting a Cisco certification like the CCNA. The CCNA does not touch on anything Microsoft related. It’s strictly network fundamentals and concepts with topics on configuring Cisco routers & switches.
From Ed Tittel (IT Certification Guy):
The preceding poster is absolutely correct in asserting that there’s no direct dependencies between the MCP/MCSE (or better yet, MCTS, MCITP, and so forth). Nevertheless, it’s not at all uncommon for local network admins to get MS credentials first, and then move on to Cisco, or for infrastructure network admins to go for Cisco first, and then move on to Microsoft credentials. Given your background, however, unless you’re dead set on doing MS Server and network management (AD, DHCP, DNS, and so forth) I’d suggest jumping straight into the Cisco stuff to see how you like it first.