The 18-year-old was detained after police saw a group shouting abuse near the away end at Anfield ahead of Shrewsbury's third round FA Cup loss against Liverpool on Sunday.
He has been released pending further enquiries according to Merseyside Police, which also said it is examining CCTV to identify any others involved.
It comes after video footage emerged of a small group, who were claimed to be Shrewsbury Town fans, chanting "f*** the 96" in Liverpool city centre.
The chant references the victims of the 1989 tragedy, although the number of lives lost has risen to 97 after the death of Andrew Devine last year. Mr Devine had suffered life-changing injuries at Hillsborough.
The teenage suspect was arrested next to 97 Avenue, which is named in memory of the victims.
Shrewsbury Town condemned the chant and said officials were working with police to identify those responsible, while goalkeeper Harry Burgoyne called for those involved to be banned for life.
A spokeswoman for Merseyside Police said: "We have arrested a man after a group of men were making abusive chants before the Liverpool vs Shrewsbury game on Sunday, January 9.
"At around 1.30pm officers approached a group of men who were shouting abuse referencing the Hillsborough disaster on Anfield Road junction of 97 Avenue.
"An 18-year-old man from Shrewsbury was arrested on suspicion of a public order offence.
"He has now been released pending further enquires."
Chief Superintendent Paul White added: “Merseyside Police are aware that any offensive chanting and behaviour were committed by a very small minority of supporters yesterday and would like to thank the overwhelming majority of fans of both clubs for their cooperation.
"Merseyside Police are investigating this incident and officers are carrying out extensive CCTV footage enquires to identify anyone involved.
“It is vital that anyone who witnesses such offences reports them to stewards or the police immediately, so we can take the necessary action.”
More than 5,000 Salop fans attended the match, which Shrewsbury lost 4-1 after going ahead through a Daniel Udoh goal early in the match.
Anyone with information can contact @MerPolCC, 101 or Crimestoppers anonymously on 0800 555111.