Spouse is already in Iceland:

A spouse may remain in the country while the application is being processed. Unless an application is being made for a residence permit on the basis of marriage or cohabitation with a student in advanced studies.

Spouse is not in Iceland:

A spouse who needs a visa to travel to Iceland may not enter Iceland until the residence permit has been granted.

A spouse who is not required to sign may enter Iceland. Unless an application is being made for a residence permit on the basis of marriage or cohabitation with a student in advanced studies.

Spouses of students:

Spouses of students of advanced studies may only stay in Iceland as long as their total stay in the Schengen Area does not exceed 90 days in the last 180-day period. If the stay exceeds this period before the permit has been granted, the processing of the application will be stopped until the applicant has left Iceland and has presented a boarding card to prove departure.

See if you need a visa to travel to Iceland.