The development comes months after Hertz announced its order to purchase 100,000 electric cars from Tesla, primarily the EV maker's Model 3 vehicles.
News of the massive deal had triggered a meteoric rally in Tesla's stock, helping it surpass $1 trillion in market value. However, Tesla boss Elon Musk later said the company had not signed a contract with Hertz.
Model Y was added to Hertz's fleet this week, news website Electrek reported on Wednesday.
Last month, Florida-based Hertz named former Goldman Sachs finance chief Stephen Scherr as its top boss, replacing interim CEO Mark Fields.
(Reporting by Aishwarya Nair in Bengaluru; Editing by Devika Syamnath)