The decision was taken after discussions with Hull Community and Voluntary Services, which manages one of the board's three pilot schemes that encourage small charities to join.
"Hull City Council was excited about the idea of protecting the public," said Jane Thompson, information services manager at Hull CVS. "Not being a member won't be grounds to withhold the public collections licence, but we are keen to promote good practice."
The philanthropic website The BigGive.org.uk, which gives details of charitable projects seeking donations of between £100,000 and £10m, also asks charities to say whether they are FRSB members when they register with the site.
Jon Scourse, chief executive of the FRSB, said: "One of our long-term strategic objectives for funders and major donors is to check whether charities applying for funds are FRSB members.