Shunin was briefly hospitalised with eye injuries after a flare landed near him during Dynamo's league game with Zenit St. Petersburg Saturday.
Fan behaviour is under increased scrutiny because Russia is hosting the World Cup in 2018.
"We want World Cup matches to take place in a wonderful atmosphere," Valcke said after meeting organisers in the northern city on Tuesday. "And also in a safe environment."
Referring to the flare episode, Valcke said: "This should not happen at the World Cup. This does not correspond to what we are fighting against."
"I can assure you nothing like this will happen at the World Cup," Valcke said.
The referee abandoned play after the incident, which has seen furious fallout.
The clubs have blamed each other and both demand the FA credit them with default victories. A ruling is expected Thursday.
Police have arrested a female fan they suspect of throwing the smoke bomb that injured Shunin.
The Russian government is trying to push through legislation that would toughen sanctions for football hooligans.
�'�'IANS/RIA Novosti
bs/dg
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors
Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share
Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor
Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements
Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app