The best puzzle games like Ico are Shadow of the Colossus, The Last Guardian and Brothers: A Tale of Two Sons. Below are 8, each with the reason it is here — and, at the end, what filtering to puzzle costs you.
Filtering to puzzle means you want to understand something rather than execute it. It is the right filter when what you liked was the click of working out how a system worked.
What you get: The moment of understanding as the reward. Good puzzle games teach a rule, let you feel clever, then show you the rule was smaller than you thought.
What made Ico worth playing in the first place is covered on the full list. This page is the puzzle part of that answer, and only the puzzle part.
The same team's next game — same silence, same world, boss fights instead of puzzles.
Team Ico's direct return to the companion mechanic, with an animal that has a mind of its own.
Two characters on one controller — the companion is a control scheme, not an escort.
Openly Ico-inspired: an island, a boy, environmental puzzles, no dialogue.
Silent, bleak, and every puzzle explains the world instead of a tutorial doing it.
A companion who is also the obstacle, in a game about something harder than it looks.
For the sparse, confident puzzle design and the trust it puts in the player.
Atmosphere and scale doing the work that dialogue usually does.
Momentum. Puzzle games are paced for twenty minutes at a time and most of them get worse past an hour.
Specifically, these are strong answers for Ico that are not puzzle games, so they are not on this page:
The full list is on games like Ico — 9 picks, no genre filter.
Shadow of the Colossus. The same team's next game — same silence, same world, boss fights instead of puzzles.
No. Ico released on the PlayStation 2, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Rarely. A friendly art style is not a difficulty setting — some of the hardest games ever made look like children's books.
In a well-designed game the piece you are missing was taught two rooms ago. If a solution only arrives by trying everything, the design is the problem, not you.
By hand. Each pick was written for the full Ico list first, on what the game actually does, and this page is the part of that list that is puzzle — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the puzzle guide for where to start in the genre generally.