The 29-year-old Spain international is currently self-isolating although he is asymptomatic.
Rodrigo missed Monday’s Premier League home defeat to Leicester City and will also sit out this weekend’s trip to Selhurst Park to face Crystal Palace.
The former Benfica and Bolton Wanderers forward will also be unavailable for the Spanish national team during the upcoming international break. La Roja are due to face Netherlands in a friendly game before Nations League matches against Switzerland and Germany.
"Unfortunately I have tested positive for COVID-19 after being in contact with a family member that had been infected without us knowing," said Rodrigo in a post on Instagram.
"As per the protocol I will be self-isolating and will miss the game with Crystal Palace.
"Both my family and I feel great, we are lucky enough to feel healthy and we are keeping a positive attitude.
"From home I will support Leeds and the Spanish National team as a supporter and I will be back on the pitch soon. Thank you for all those who have shown concern."
Rodrigo joined Leeds United from Valencia in a club record £28m deal in August and has so far scored one goal in seven appearances across all competitions.
