Promoter Frank Maloney has confirmed that the former world featherweight champion will not be making his ring comeback next week.
The 34-year-old has been away from the sport for more than six years due to personal problems and was set to resurrect his career on Maloney's bill in Blackpool on March 31.
However, those plans have been scuppered following Harrison's arrest on Wednesday in connection with an alleged theft at a supermarket in Rutherglen, near Glasgow.
Promoter Maloney has decided to drop the Cambuslang fighter Harrison, whom he managed when he was at the top of his sport.
But Peter Harrison said in a statement that his son intended to be back in the ring "as soon as possible", so he can support his fiancee and three children.
Peter Harrison said: "Regarding the cancellation of Scott's fight, which was scheduled for Saturday the 31st of March in Blackpool, I would like to make it clear that Scott did not pull out of the fight.
"Scott trained as usual on Tuesday afternoon in the gym. There has been a lot of media coverage regarding an incident in the early hours of Wednesday morning and it would be inappropriate to comment on that at the moment.
"However, Scott resumed training on Wednesday by running from Cambuslang to the Cathkin Braes and remained committed to boxing in Blackpool on Saturday the 31st of March.
"It is public knowledge there is a legal battle over who does and does not have a legal right to promote Scott."
Rival promoters Maloney and Frank Warren have both claimed entitlement to put on fights for Harrison.
Peter Harrison added: "This has weighed heavily on Scott's mind and caused a great deal of stress over the last two weeks.
"It took quite a while for Scott to regain his boxing licence and after all the time and effort it looked as though he was set to make his return to the ring.
"Then the legal battle started and, with all the speculation, it had a negative impact and Scott was faced with the scenario that he might not be able to box.
"Scott has three young children and a fiancee to support and is determined to box so he can earn money to provide for them. The prospect of him being denied the opportunity to do this has clearly been very damaging.
"Although it will not be on the 31st of March, Scott still intends to continue his boxing career as soon as possible."
In December Harrison vowed to challenge for a world title when the British Boxing Board of Control made the decision to grant him his licence after his case was backed by the Scottish Boxing Area Council.
The Scot has not fought since he successfully defended his WBO featherweight belt in November 2005 against Nedal Hussein.