The Valiants were issued with the order by HM Revenue and Customs over an unpaid tax bill, with a case set to be heard on August 18 in London.
But Smurthwaite has claimed the petition will not affect the running of the football club and feels the issue has already been resolved.
He told the Stoke Sentinel: "This is a clerical error going back to 2012/13 and is the old company. PVFC Ltd is being wound up anyway, it is a company that is no longer trading. It doesn't affect Port Vale Football Club Limited.
"This has been sorted and the Inland Revenue aren't owed money anyway.
"It was a clerical error and there is no risk to the football club."