CRCC was at the head of a consortium that had won the project last year, which was abruptly revoked shortly after being awarded.
The deal was called off over controversy in the bidding process.
The Mexican government relaunched the bid earlier this year, but that was cancelled for a second time.
The second cancellation of the 130-mile rail link was blamed on budget cuts.
The Chinese rail firm gave Mexico's communications and transport ministry (SCT) a list of costs that it had incurred during the bidding process and had requested for compensation.
The ministry announced the amount to be paid to the firm on Thursday.
If the deal had gone ahead, it would have resulted in Mexico becoming the first Latin American nation to have a bullet train after Brazil and Argentina had postponed their own rail projects.
Mexico will compensate China Railway Construction Corporation (CRCC) $1.31m (£835,953) for cancelling a $3.75bn high-speed rail contract.