Highland Council has already announced it will also appeal against the decision by the Scottish Government's planning reporter.
Ministers granted permission to the scheme but a legal challenge by Mr al Fayed, who owns the nearby Balnagowan Estate, led to a public inquiry.
The inquiry reporter concluded that, although public concern was widespread and sincere, it did not warrant the refusal of planning permission.
Mr Fayed's Ross Estates Company has now lodged grounds of appeal, citing a failure to take proper account of the impact of the incinerator on road safety and a failure to assess an alternative site.
Mr Al Fayed said: "I am determined to stop this thoroughly undesirable development."