The 22-year-old world number 25 hopes the painful intervention will get him fit enough in time for the French Open, the season’s second Grand Slam which gets under way in Paris on May 27.
Kyrgios said he has been suffering the injury since February’s Davis Cup clash against Germany in Brisbane and has since played just two events.
“I have done everything in my power to overcome this organically through rehabs, rest and treatment but have still been suffering with pain,” the Australian wrote in a statement on Twitter.
“I have been unable to play anywhere near the level I need to be at to compete at the highest levels.
“I have now taken the advice of my physio and doctors to have a cortisone injection directly in to the elbow.”
Kyrgios will now miss Estoril, where he played his first final in 2015, which starts on April 30 and the Madrid Masters from May 6.