The outgoing US President confirmed in a Sunday afternoon tweet that the former New York mayor had caught the virus.
Mr Giuliani has travelled extensively to battleground states in recent weeks in an effort to help Mr Trump challenge his election defeat.
Mr Trump wished him a speedy recovery.
“Get better soon Rudy, we will carry on!!!” Mr Trump wrote in his tweet.
Mr Giuliani attended a hearing at the Georgia Capitol on Thursday where he went without a mask for several hours. Several state senators also did not wear masks at the hearing.
On Wednesday night, the lawyer was in Lansing, Michigan, to testify in a highly unusual four-hour legislative hearing in which he pushed Republican lawmakers to ignore the certification of Joe Biden’s Michigan victory and appoint electors for Mr Trump.