According to the official medical disqualification list for the Marines and the Army, a heart murmur may permanently disqualify you, but not necessarily. It really depends on the severity of the murmur and whether it's connected to any other heart conditions. If you're in stellar health and the murmur doesn't have an impact on your physical activity level, you may still qualify for service.
Applying With a Heart Murmur
One of the first things your recruiter will do when you start your application process is hand you a list of questions about your medical history. These questions include a question about a heart murmur, valve problem or mitral valve prolapse, along with another question about an irregular heartbeat. You may be required to present proof from you doctor that the heart murmur isn't serious or is no longer present.