"We're very excited about the timeline," Mnuchin said on "Squawk Box." "We're going to have the Senate, as soon as they get back from Thanksgiving, vote on the bill."
"We have every reason to think it will get to the president's desk before Christmas for him to sign," he added.
House Republicans passed a monumental bill to cut taxes on businesses and individuals on Thursday in the GOP's once-in-a-generation effort to overhaul the American tax system. The plan passed by 227-205.
Trump tweeted late Thursday about the bill passage, calling it a "big win" for the House.
@realDonaldTrump: Big win today in the House for GOP Tax Cuts and Reform, 227-205. Zero Dems, they want to raise taxes much higher, but not for our military!
Mnuchin said on CNBC Friday that the House tax bill will place a higher burden on those who earn more than $1 million per year but provide a break to everyone else.
Meanwhile, members of the Senate Finance Committee voted to approve their version of a tax package late Thursday. The approval is seen as a crucial step for the Senate to consider the bill after Thanksgiving.
But complicating matters for the Senate is a Joint Committee on Taxation analysis released Thursday, which says that average taxes for all income groups would go up by 2027 after initially dropping under its plan.
Mnuchin maintained on CNBC Friday, "The focus of the plan really is middle-class tax cuts and delivering those right away and making our business tax system competitive."
The objective of the plan is to simplify taxes and level the playing field, he added.
As a result of rules on Capitol Hill, Mnuchin said, "There are certain parts of this that expire, but we have every expectation that down the road, Congress will extend them."
If the Senate is also able to pass its bill, congressmen and senators would then work to reconcile the measures and craft one piece of legislation. If that were to pass both chambers, it would go to Trump for approval.