You don’t ordinarily praise a monster movie for a sense of balance and proportion, but then “The Host” is not your ordinary monster movie. Bong Joon-ho, the Korean director of 2003’s unforgettable policier “Memories of Murder,” has again nurtured a genre premise into smart, fresh, and gripping work that continually surprises with an effortless range of interests.

At last year’s Toronto and New York Film Festivals, “The Host,” already Korea’s highest-grossing movie of all time, was relegated to midnight-movie slots, a classification ill-suited to the polished product. Not only are the creature thrills of “The Host” superbly executed and inventive, they’re part of a broader canvas: dysfunctional characters, robust satire of authority, unexpected comedy, intriguing working-class sympathies, and a gorgeous feeling for space and camera placement.

It all starts with a king-sized walking fish. In a delicious sins-of-modernity premise à la “Godzilla,” a U.S. Army base dumps toxic waste into Seoul’s Han River. Nature takes its wondrous course, and soon enough an endearingly lopsided mutant amphibian is spotted dangling from a river bridge. The huge, shadowy blur is hard to make out precisely, especially once the thing slips into the water. The official public response at this point: Throw stuff at it.

Unfortunately for them (fortunately for us), the beast gets hungry. Pandemonium erupts at the riverside park as it comes ashore, and Mr. Bong puts on a fantastic show. The truck-size creature, ever teetering forward like a raptor, galumphs in and out of view through the scrambling crowds that become his movable feast. The bravura sequence, featuring a foolhardy last stand and some grisly hide-and-seek, is an on-the-run spectacle to place alongside “Jaws” (which it obviously cites) and “War of the Worlds.”

Despite the grand entrance, we never quite get a bead on the monster, even when it’s in view. This isn’t a coy horror-movie trick, though the uncertainty does add to the terror. In Mr. Bong’s treatment, the monster is not the main event — a freakshow wheeled out for our titillation and delectation. “The Host” is soon too busy spiraling the chaos outward into a bedraggled family’s attempt to rescue a bratty daughter and the government’s hectic imposition of order and secrecy.

The missing child, Hyun-seo (Ko Asung), who is snatched by the monster in the opening raid, belongs to 30ish dullard Gang-du (Song Kang-Ho, the star of “Memories of Murder”). He works, or worked, with his ornery father at the family seafood shack, sporting a brain-dead dye-job and a shuffling gait. His sister is an archer who chokes in competition, his brother a tetchy, unemployed university grad. At a public mass memorial in a gym, they roll around in grief, half pathetic and half comic.

Not exactly a bunch you’d put money on to save the day, and their ineffectual backbiting and class abjection shows that “The Host” won’t be a Spielbergian nuclear-family-takes-all. When Gang-du tells officials in hazmat suits that he touched the monster, he’s whisked into quarantine with his family, bullied by petty personnel, and prodded by a spooky American surgeon. The protracted escapes that ensue hinge not on spunky heroism but helpless arrangements with opportunistic thugs.

But back to the monster: Hyunseo plays possum at the bottom of a dungeon-like culvert that serves as the beast’s nest and corpse depository. What Mr. Bong accomplished in the sun-kissed open-air chase he matches in the creeping terror and suspense as the beast comes and goes. Its CGI-derived behavioral nuances express the grace and viciousness of any wild predator instead of pushing demonic evil. I even grew a little fond of the dumpy yet surefooted slimeball, who trapezes from strut to strut on the Han River bridge and engages in hellacious regurgitation.

The family eventually gets it together to make rescue attempts, edged with futility, while the government sprays “Agent Yellow” to dispel mounting fears of monster cooties. Throughout, Mr. Bong pockmarks his scenes with bits of black comedy, slapstick that is never very comforting, and desperate fatigue. The little change-ups in tone befit the crisis and bring out the family’s frustration.

The film’s jabs at America join a tried tradition and ultimately target the South Korean government as well; frankly, Mr. Bong dishes a little out to everyone. “The Host,” like any good genre movie, works whether or not you think too hard about its connection to reality. What’s refreshing is how it confounds expectations not as a means to a twist, but because things don’t always work out in life. Sometimes that’s because of a monster pollywog.