The 59-year-old, who coached Ukraine at Euro 2012 where the co-hosts failed to reach the knockout stage, was admitted to hospital on Friday with high blood pressure.
He was operated on for a thrombosis of the left carotid artery, doctors were quoted as saying by the Sports.ua website.
"The surgery was a success. Oleg Blokhin feels like one should feel during a post-operational period", said Mykhaylo Radutsky, the head of the medical team.
"Thrombosis of the carotid artery can develop into a stroke. A person needs around two weeks to a month to fully recover after an operation", a surgeon, Taras Pavlenko, was quoted as saying.
"He had to have an immediate surgery after we checked his condition," hospital chief Mikhail Radutsky told the club's website (www.fcdynamo.kiev.ua).
Dynamo president Igor Surkis added: "Blokhin was conscious when I saw him after the operation, he recognised me. I hope the worst is already behind him."
Ukraine assistant coach Andriy Bal will prepare the team for their 2014 World Cup qualifiers away to Moldova on Oct. 12 and home to Montenegro four days later which were supposed to be Blokhin's final games in charge after he joined Kiev last month.
Blokhin, who played for the former Soviet Union and was voted the European Footballer of the Year in 1975, guided Ukraine to the 2006 World Cup quarter-finals.
He resigned as national team coach last week after accepting the Dynamo job and led the club, Ukrainian league runners-up, to a 2-0 Champions League win over Dinamo Zagreb on his European debut at the helm earlier this week.