My (admittedly limited) knowledge is military ships are generally built to withstand a blast that far away. Provided the crew were expecting it, hatches and air vents closed, filtration systems working, etc, they should be ok at that range, even if they're in the fall out zone.
Once they're out of the area they'd have to do some serious decontamination and scrubbing though and there may still be some residual radiation after that. Anyone who stays inside should be safe enough.
Only those on deck, or not shielded by the superstructure would probably be injured (3rd degree burns, knocked off their feet if outside). Anyone on the bridge if shutters were not in place would likely be injured.
http://nuclearsecrecy.com/nukemap/?&...angle=99&zm=11
Sample point is 10.3 km from ground zero.
Overpressure: 4 psi
Maximum wind velocity: 62 mph
Initial radiation dose: 0 rem
Thermal radiation: 34.7 cal/cm²