The sanctions are directed at the Bank of Dandong, a Chinese lender that Treasury officials say acts as a conduit for illicit North Korean financial activity.
He wrote: "While I greatly appreciate the efforts of President Xi & China to help with North Korea, it has not worked out". He said that "nobody is off limits" when it comes to giving illegal financial assistance to North Korea.
The moves come in response to North Korea's ongoing efforts to build missiles and its violations of U.N. Security Council resolutions.
The Treasury Department says that the Bank of Dandong is a "primary money-laundering concern".
The sanctions also come one week after the U.S. and China failed to announce a joint action plan to freeze North Korea's nuclear programme after their first Diplomacy and Security Dialogue in Washington, but reached a consensus on not doing business with any UN-designated North Korean entities.
The president was to meet for the first time Thursday with South Korea's new leader, President Moon Jae-in, who has long advocated outreach to North Korea.
President Donald Trump is growing increasingly frustrated with China over its inaction on North Korea and bilateral trade issues.
"The takeaway is China is still not doing what China needs to be doing, and while we're working with them in a very cooperative way right now, my sense is if they don't step up soon we're going to then move to the coercive mode, which means secondary sanctions", Corker said.
Anthony Ruggiero, a sanctions expert and former Treasury Department official, described it as a small Chinese bank "sitting at the heart" of trade between North Korea and China.
-Chinese national Li Hong Ri, said to have established several front companies that end up benefiting Koryo Bank, a USA -sanctioned conduct for financial transactions on behalf of North Korea.
On North Korea, Mr Trump "feels like he gave China a chance to make a difference" but has not seen enough results.
A Treasury statement named the bank as the Bank of Dandong and the firm as Dalian Global Unity Shipping Co Ltd.