Japan had enough chances to have won comfortably but were let down by poor finishing and some fine saves from Swedish goalkeeper Hedvig Lindahl.
It means that the Swedes, beaten by Japan in the 2011 World Cup semi-finals, still head the group on goal difference from their opponents.
Japan were on the offensive from the first whistle and produced some fluent football but were unable to create any clear-cut opportunities in the opening 45 minutes.
Swedish captain Sara Thunebro was shown a yellow card after 21 minutes for holding back Yuki Ogimi in a low-key first half.
Japan were more threatening after the interval with Lindahl turning aside a curling effort from Nahomi Kawasumi and saving a low effort from Homare Sawa to her left.
It was one-way traffic towards the Sweden goal and Lindahl was well positioned to cling on to Ogimi's drive after a mistake by Caroline Seger.
Shinobu Ohno should have scored after 69 minutes but failed to make full contact on her close-range effort from Yukari Kinga's centre.
Then Kawasumi cut inside but dragged her shot wide.
Sweden coach Thomas Dennerby said: 'Overall I am very satisfied with the result because now we have four points and a better goal difference. The situation is very good for us.
'There is a big opportunity for us to come out of the group after getting a point against the world champions.'
Japan coach Norio Sasaki said: 'For the first half I was not satisfied with with what happened and during half-time I told them to deal better with their opponents.
'In the second half the offense was very quick and we had good chances and the players were very aggressive. I was satisfied with the attitude of our players.'