CSKA coach Leonid Slutsky said he was hoping European football's governing body would allow his players to wear the armbands in memory of 39 people killed after two female suicide bombers detonated bombs on packed metro trains during rush hour on Monday.
Moscow officials declared Tuesday a day of mourning.
The national flags were flying half-mast, while cultural institutions, TV and radio stations cancelled entertainment programmes and activities.
Russian President Dmitry Medvedev also cancelled Tuesday's Kremlin reception for medal winners of last month's Paralympic Games in Vancouver.
"This is a real tragedy," Slutsky told reporters in Milan, where his team was preparing for Wednesday's quarter-final, first leg tie against the Italian champions.
"We all feel the grief. It's not only Moscow, it's a tragedy for the whole of Russia. We all hope that such terrible senseless things would never happen again."
Russian basketball champions CSKA Moscow said they also would wear black armbands in their Euroleague quarter-final away to Spain's Caja Laboral on Tuesday as a mark of respect for the victims.
European Union leaders condemned the bombings and U.S. President Barack Obama called the Kremlin to offer condolences.
The International Olympic Committee (IOC) sent its condolences to the victims and their families.
The IOC also expressed confidence in Russia's ability to provide a safe Winter Olympics in Sochi in 2014.
Security has been one of the major concerns since Sochi was awarded the Games in 2007 because of the Black Sea resort's proximity to the volatile Caucasus region.
But the IOC said it was "confident the Russian authorities will put in place all necessary measures to ensure that the Olympic Winter Games in Sochi are held in a safe environment."
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