Nolan sustained a torn hamstring in last week's draw at Burton and although not first thought to be serious, scan results have confirmed a muscle tear.
He now joins fellow right-back Christian Ribeiro on the sidelines, leaving on-loan Cliff Byrne as the club's only other recognised right-back.
Laws told BBC Radio Humberside: "Eddie's results weren't what we expected.
"He had a scan on Tuesday and it has come back with a tear on his hamstring, which unfortunately for him, and for us, will put him out of action for around six weeks.
"It may mean that we have to look at adding one or two players on loan, but we have the two-week gap after Cheltenham, so we won't rush and we will make sure we get the right man."