Hewitt was charged in January for engaging in offensive conduct towards a doping control official after he pushed a 60-year-old volunteer anti-doping chaperone following Australia's semi-final loss to Italy last November.
The former world number one, who was also fined A$30,000 ($19,803) by the International Tennis Integrity Agency (ITIA), told reporters on Thursday the matter was now with his lawyers.
"I'm just really disappointed about the overall decision but also the whole process to be honest, and the lack of facts that have been put out," he said ahead of Australia's Davis Cup tie against Belgium.
"But I'll be going to the appeal process with my legal team, so I won’t be talking about it any further."
Hewitt's ban, effective from September 24th to October 7th, will prevent him from taking part in all tennis-related activities, including coaching, mentoring, playing, captaincy and other associated roles.
Hewitt said he would not make the issue a distraction for Australia's home Davis Cup tie against Belgium this weekend, "unlike the ITIA and ITF (International Tennis Federation."
The former Wimbledon and US Open champion confirmed John Peers, Aleksandar Vukic and Davis Cup debutant Rinky Hijikata have been included in the Australian team, while Alexei Popyrin and Matt Ebden are unavailable due to injury.
"Really excited for Rinky, it’ll be his first time wearing the green and gold, and for him to get the opportunity playing at the place where he grew up, in Sydney, is something really special," he said.