The fund had been facing a legal wrangle with Japan's financial regulator in order to secure the deal - and indicated in a statement that this "lengthly judicial process" was a contributory factor in its decision.
TCI currently holds a 9.9 per cent stake in the power wholesaler - just under the ten per cent legal limit for overseas acquisitions in firms "vital for national interests" that is enforced by Japanese law.
In its statement, the fund criticised the nation's regulators as "flawed by erroneous fact-finding, unsound economic reasoning, misinterpretations of law and a lack of transparency".
Responding, Japan's vice trade minister Harufumi Mochizuki said: "Nothing has changed with our trade policy, aimed at making Japan a more open market and promoting overseas investment.
"In TCI's J-Power bid, we've found a national security issue, and our rejection of the proposal was an exceptional case."
TCI currently holds around $10 billion in assets, Bloomberg reports.