HM Revenue and Customs official raided Murphy's house on Tuesday morning and the 34-year-old, along with his wife, were arrested on suspicion of evading income tax and VAT and cheating the public revenue.
HMRC told Sky Sports News in a statement: "Computers, business and personal records were seized during the operation. The couple were interviewed by HMRC and have both been released under investigation. Investigations are ongoing."
Murray joined Brighton last year from Bournemouth in a £3m deal, having initially left for the Cherries from Crystal Palace in 2015.