The Breaking Bad star said he has since recovered from the virus and is now donating his plasma to help others.
Cranston considers himself "one of the lucky ones", as he only had "mild symptoms".
Best known for his role as Walter White - the chemistry teacher in AMC's Breaking Bad series - the actor is seen visiting the blood and platelet donation centre at the University of California, Los Angeles.
In a video to the social media platform, Cranston explained he tested positive to the virus a "little while ago" and outlined his symptoms which included headaches, tightness of the chest and loss of both taste and smell.
Bryan Cranston accepts the award for best performance by an actor in a leading role in a play for "Network" at the 73rd annual Tony Awards at Radio City Music Hall on Sunday, June 9, 2019, in NY.
"Hi. About now you're probably feeling a little tied down, restricting your mobility and like me, you're exhausted of this!" he wrote. "Well, I just want to encourage you to have a little more patience", he wrote.
In the Instagram video, Cranston wears a surgical mask as a phlebotomist at the UCLA Blood & Platelet Center draws blood from his right arm. I was pretty strict in adhering to the protocols and still. "I contracted the virus", Cranston wrote in the caption to the Instagram post. He said the process took about an hour, during which he watched "A Face in the Crowd" starring Andy Griffith and Patricia Neal. I was one of the lucky ones.
So, the actor's encouraging people to remain patient and vigilant - and keep following the rules - in order to prevail through this pandemic.
Ruth Bader Ginsburg Back in Hospital Following Cancer Diagnosis
The court has a 5-4 conservative majority, with two justices appointed by Trump-Brett Kavanaugh in 2018, and Neil Gorsuch in 2017. The 87-year-old justice, who has had past health scares, is customarily transparent to the public about her medical history.