After an out of state DUI, am I required to have an ignition interlock installed on my car before they will issue me a license?

Only the state that issued your license can impose restrictions on it.  Moreover, the state in which you were charged with the dui can only suspend/revoke/restrict your ability to drive in their state.

However, if the state that did not issue your license suspends your license to drive in their state, your state may recieve notice and suspend your license in your state.  But, your state has its own statutes that govern restrictions that may apply to you.

I recommend that you call the DMV in your state and see what restrictions may or may not have been applied to your license.

Hope this helps.