The leak in Unit 2 is not radioactive and not a threat to the public, said a spokeswoman for the plant, which is 50 miles west of downtown Phoenix.
That brings the plant, a crucial source of electricity for the valley, down to one operating reactor.
Unit 3 is undergoing a scheduled refueling and steam-generator repair that is expected to keep it off-line for 75 days.
Unit 2's cooling-water leak should be repaired quickly and the reactor could be at full power very soon, said Betty Dayyo, an Arizona Public Service Co. spokeswoman. The utility operates the facility for several owners.
Unexpected outages can affect the price Arizonans pay for electricity because they force utilities to buy or generate more-expensive energy to replace the relatively cheap energy generated at Palo Verde.
APS can turn up some of its natural-gas-fired power plants in the region that are not running at capacity to make sure Arizonans have enough electricity, Dayyo said.
"We're looking at the costs between our own units and what the market (price for electricity) is," Dayyo said.
A Salt River Project spokesman said that it likely will cost the utility and its customers more to replace power that utility normally gets from Palo Verde but that it is difficult to determine how much this early in the outage.
"Our resources are plenty to meet customer demand," SRP spokesman Scott Harelson said.
Most of the Valley is served by APS or SRP.
Separately, an independent audit of reactor problems in 2005 and 2006 at Palo Verde's Unit 1 caused by a vibrating cooling pipe found that APS' actions were "reasonable and prudent" in handling that expensive problem.
GDS Associates Inc. of Georgia reviewed the problem and determined that it could not have been anticipated and that repairs were made "in a reasonable amount of time."
It cost APS $79 million to replace the power lost during that episode, and it has been collecting the increase from ratepayers.
If the GDS report showed the utility acted irresponsibly, regulators might have been more likely to ask the utility to refund the money.
GDS has previously determined that some earlier outages at the plant were the utility's fault, and it recommended against allowing APS to collect higher energy costs.
"APS believes that all replacement power costs (from the vibrating-pipe outage) were prudently incurred and that... (the money) will not have to be refunded," APS spokesman Alan Bunnell said.