Woodward, who led England to victory at the 2003 tournament, described the risk of "one stupid tweet" to squad harmony as "the new enemy".
Hosts England start their 2015 campaign against Fiji on 18 September.
"If you allow one player to be distracted, it can all come tumbling down," said the 59-year-old.
Speaking to the Radio Times, Woodward added: "We didn't have to worry about it in 2003. I've had the conversation with Stuart Lancaster.
"Don't let the players be distracted. It could be the media, their family, sponsors, ticket requests, anything."
England have reportedly handed their World Cup squad social media guidelines, keen to avoid any unnecessary distractions.
Meanwhile, Rugby Football Union chief executive Ian Ritchie has refused to be drawn on what Lancaster needs to achieve at the World Cup to retain his job as England coach.
"I'm not going to deal in hypotheticals," he said. "I think we should be going into every game trying to win it and I think that's what we'll try and do.
"We are in here to try and win the event, we will worry about the hypotheticals afterwards.
"Knowing the squad and the coaching set-up, they are all very focused on doing their very best to win and I think we have a chance of doing that."
Listen to 'Woodward's World Cup' on BBC Radio 5 live on Wednesday, 9 September from 21:00 BST.

They will also face Montpellier, now coached by former Scotland team boss Vern Cotter, and Leinster, who were second in the Pro12 table last season.
Montpellier finished third in the French Top 14.
The first pool match will be on either 12/13/14/15 October, with the final on Saturday 12 May in Bilbao.
Glasgow reached the quarter-finals for the first time last season after home and away victories over both two-time European champions Leicester and French giants Racing 92 in the pool stages.
The Warriors finished runners-up to group winners Munster, and were beaten by eventual champions Saracens in the last eight.
Glasgow beat Montpellier home (21-10) and away (15-13) when they met in the pool stages of the 2014-15 Champions Cup, and also overcame Exeter twice in their group the previous season, winning 20-14 at home and 15-10 at Sandy Park.
Leinster are familiar foes in the Pro12, with Warriors beating the Irish province 33-25 at home last season, before losing 31-30 at the RDS in Dublin in late April.
The last time they met in Europe in 2011-12, Leinster prevailed home and away to finish top of the group on route to their third European title in four seasons.
Glasgow were distant runners-up, having also beaten Montpellier at home and drawn away in the same campaign.
Glasgow's new forwards coach Jonathan Humphreys, who worked alongside Cotter with Scotland before moving to the Warriors this summer, said he had a sense of inevitability about the draw.
"We talked to Vern about this a fair bit during the Six Nations - we were convinced it was going to happen!" he told the Warriors website.
"We've worked together for a long time, so we know what the strengths and the style of play of Montpellier will be, although we said we would double-bluff each other.
"It's a really exciting group and we're looking forward to it. Leinster, Exeter and Montpellier all want to play a good brand of rugby."
Former England head coach Sir Clive Woodward has warned current boss Stuart Lancaster that social media could derail his side's World Cup campaign.
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Glasgow Warriors have been drawn against English Premiership champions Exeter Chiefs in their four-strong European Champions Cup pool.