"Today, Dykan had a medical examination which revealed damage to a shoulder joint. He will be out of action for a month," Spartak said on their website.
The 35-year-old Ukraine international sustained the injury in Saturday's 3-1 Russian league victory at Amkar Perm.
Spartak, beaten by Barcelona 3-2 in their Group G opener this month, face Scottish champions Celtic in Moscow on Tuesday before hosting Portugal's Benfica on October 23.
The Muscovites already have several key players out with injuries, including captain Sergei Parshivlyuk, Brazil international midfielder Romulo and leading striker Welliton.