The letter, penned by the firm's chief executive Dave Clark, said that the e-commerce giant stood "ready to assist you in this effort".
Amazon has come in for criticism about its handling of the pandemic, with some staff claiming conditions in its warehouses were not safe.
But it is also asking for vaccines for its workers to be prioritised.
The firm has signed an agreement with an unnamed healthcare provider to administer vaccines on site at its warehouses around the US. It has requested that its 800,000 workers around the world be among the first to receive the doses, because they are unable to work from home.
President Biden has vowed to deliver 100 million Covid-19 vaccinations to US citizens in the first 100 days of his administration.
In the letter, Mr Clark wrote: "We are prepared to move quickly once vaccines are available."
He said the firm was ready to "leverage our operations, information technology, and communications capabilities and expertise" to assist in the effort.
"Our scale allows us to make a meaningful impact immediately in the fight against Covid-19 and we stand ready to assist you in this effort."