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".
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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.
A football club has criticised searches of its female supporters who were asked to show their bras to security staff.