Grimsby Town said it "fully supports the letter" issued by fan group the Mariners Trust to Stevenage FC.
The Mariners Trust made the allegations about the treatment of some fans after the two sides met on Saturday.
Stevenage FC said it implemented "a full, 100% compliant, searching regime" after fears of "the potential for anti-social and un-cooperative behaviour".
More on this and other Grimsby stories
In response, Grimsby Town said that after being contacted by the Hertfordshire club it reassured them "that risk issues would be minimal".
The club added: "It was suggested to Stevenage that positive engagement would result in a fun and issue-free day and that the only small risk they faced was a chance of smoke bombs from a small section of younger supporters aged 15-25, as this happened at Chesterfield."
"GTFC does not condone searching of minors (under 13s) or the questioning of females about the contents of their underwear."
The letter from the supporters' group alleged stewards asked some female fans "if they could feel their bras" if they told them they were were underwired.
It claimed the searches were "in full view of male stewards, fans and police" and described them as "a gross invasion of privacy".
The fans group also said children as young as five were subjected to full body searches and supporters had items confiscated that were not listed as being banned, such as "contact lens solution, cough sweets and medication".
Stevenage FC said the searches were implemented because "after liaising with Grimsby Town's safety officer, the police and others, it was indicated that prohibited items were likely to try to be brought into the grounds and could be passed onto those deemed less likely to be searched, such as women and younger supporters".
Grimsby Town said it would be raising the issue with Stevenage.

The last school in the borough to teach A-levels, Halewood Academy, announced last year that it could no longer afford to offer the qualifications.
It prompted complaints from parents in a borough that already had among the UK's lowest rates of university entry.
The plans would see the building of a new dedicated centre for A-levels.
A delegation from Knowsley Council has held meetings with the Department for Education, the Education Funding Agency and local MPs.
The councillor responsible for education, Joan Lilly, was "very hopeful" about plans for building a new A-level centre in the borough, with a final decision expected in May.
The loss of A-levels in an entire local authority became a high-profile issue, with claims that it showed social mobility was going into reverse.
Since A-levels were introduced in the 1950s, it was unprecedented for a borough not to be able to offer the qualifications.
It means that teenagers from the borough, wanting to take A-levels, have to try to get places in schools in other authorities.
It also raised questions about how schools were organised locally - as the council had no control over an academy being able to decide to stop teaching A-levels, even though it ended all A-level provision in the borough.
The decision to allow the closure was then approved by central government.
Halewood Academy's decision also highlighted problems with funding - as the academy said that it was not financially viable to deliver A-levels, once its sixth form had fallen below a "break-even" point of 155 students.
Vanessa Pointon, part of a parents' campaign against shutting down the sixth form, had said: "This is letting down the children of this community. There are people who want to go to university, lots of kids who want to do well."
Joan Lilly, the council's cabinet member for children's services, said there seemed to be confidence in plans for a new place to study A-levels.
"The council has been working hard to raise standards in all our secondary schools, and with the establishment of the Knowsley Education Commission the Department for Education seems confident that these efforts will begin to have an impact in the near future.
"It is only right, then, that we work together to ensure that pupils have a top-quality centre in which to study A Levels here in the borough - and that is what we are very hopeful that we will achieve."
A football club has criticised searches of its female supporters who were asked to show their bras to security staff.
[NEXT_CONCEPT]
Knowsley is planning to offer its young people A-levels again, with government and local representatives holding meetings over a new A-level centre.