Woodward, who led England to World Cup glory in 2003, wrote in a column for the Daily Mail that the 2019 World Cup has become "a retirement party for many coaches of the leading contenders", and says it was a huge mistake which could hand Eddie Jones and England the advantage heading into the tournament.
"The All Blacks always seem to make smart decisions on and off the pitch, so I am genuinely surprised by them," Woodward wrote in the Daily Mail.
"Having zero distractions is key and this is a major distraction for the coach, team and country. Players will wonder and continually be asked: "Who is going to be in charge next?".
"I want coaches saying: "I love this job, if you don't want me, fire me". If you're considering stepping down, leave any announcements until after the tournament.
"I want total focus on winning the World Cup, moving on if successful and creating a dynasty.
"I signed a four-year contract in 2003 before we went to Australia simply because I wanted no distractions. It totally focused my mind.
"We now have a bunch of top coaches thinking about their next role. It's weak. England must not get involved in this coaching sideshow, it really does give them an unexpected advantage."
Woodward, who is considered as one of the best rugby coaches in history, brought up the example of former Manchester United manager Sir Alex Ferguson, and his initial decision to step away from the club.
"I remember when Sir Alex Ferguson announced he was retiring from Manchester United in 2001. I had always admired his career and at the time thought it was very strange, 'un-Ferguson like'," Woodward wrote.
"United crashed out of the FA Cup and League Cup early and finished third in the league — 10 points behind Arsenal.
"In early 2002 Ferguson performed a U-turn and stayed, admitting that focus was lost after his announcement.
"'A lot of players put their tools away,' he said later. 'They thought, "Oh, the manager's leaving" but when I changed my mind I started thinking about United again and how we could get back on top.'
"That quote totally reinforces my view."
Woodward finishes his column by emphasising the point that departing coaches Hansen, Rassie Erasmus, Warren Gatland and Joe Schmidt will end up being a distraction for their respective teams.
"In 2019 it will all be about Hansen, Erasmus, Gatland and Schmidt whether they like it or not. A key first test of this will be Ireland v England in the opening round of the Six Nations. If England can keep their powder dry, focus on the next game and not the next coach, I see them beating Ireland. Now that would be an amazing start to a brilliant year in Test rugby."