The result leaves Sweden on top of Group F on goal difference, with Japan in second place. Canada plays South Africa later Saturday in the second Group F game of the day.
Japan created a multitude of chances — especially in the second half — but were unable to take advantage, with Sweden goalkeeper Hedvig Lindahl making several saves to keep the game scoreless.
"There were some mistakes but overall they created chances and integrated well and I am satisfied with the players," Japan coach Norio Sasaki said. "I really wanted them to have the three points but Sweden is a very good team so I am satisfied with the result."
Yuki Ogimi had the first attempt on goal with an acrobatic volley which failed to hit the target. Caroline Seger had the best chance for Sweden in the first half, when her powerful shot was blocked by Homare Sawa for a corner.
Japan came out with more attacking intent in the second half, and Lindahl had to make her first real save just two minutes after the break on a stinging shot from Nahomi Kawasumi.
Lindahl was forced into action again two minutes later, when some intricate link up play ended with an effort on target from Sawa.
Shinobu Ohno had two opportunities to score, but her weak efforts were too easy for Lindahl.
Sweden created few chances in the second half, with Lotta Schelin's effort stopped by Fukumoto in the 70th and substitute Kosovare Asllani heading wide of the goal three minutes later.
"It was a fair result. They are two good teams," Sweden coach Thomas Dennerby said. "It was slow in the first half but faster in the second. I am very satisfied with a point. Now we have got four points. The situation going forward to the knockout stage is very good for us."
The game at the City of Coventry Stadium was a rematch of the 2011 World Cup semifinal, which Japan won 3-1.