Barca, who suffered a shock 2-1 defeat by the Russians at the Nou Camp two weeks ago, missed the best chance in the second minute when Zlatan Ibrahimovic raced on to an Andres Iniesta pass and hit the post.
The draw leaves both teams on five points from four games in a tight Group F ahead of the match between Dynamo Kiev (four points) and Inter Milan (three) later on Wednesday.
"How can I be unhappy if we took four points off Barcelona, the best team in the world," Rubin coach Kurban Berdyev told Russian television NTV.
"Our plan was to contain Barca and try to hit them on the break. We were able to execute it to perfection in Barcelona and we came close to repeating the same trick here."
The busy Ryzhikov also denied Iniesta and Ibrahimovic before the interval.
RARE THREAT
Barca keeper Victor Valdes did well to keep his concentration when faced with a rare threat, stopping Alexander Ryazantsev's low drive late in the first half.
Barca's last chance fell to substitute Thierry Henry and his left-foot shot flew well wide.
"We have two matches left and we'll have to see how we respond," coach Pep Guardiola told a news conference.
"We knew the group was going to be difficult and the Russian teams are very well organised. We know what we have to do now, get the six points, and if we don't it'll be because we didn't deserve it."
Midfielder Iniesta said: "It's a shame. The team played well and all we were missing was a goal. We had quite a few chances but we didn't manage to convert them."
