Altermagnetism, a moment-compensated magnetism with momentum-dependent spin splitting, has so far been realized primarily in Néel-type antiferromagnets. Here, we demonstrate altermagnetism in folded iron-chain systems with block-type magnetic order (e.g., ↑ ↑ ↓ ↓). In the strictly one-dimensional (1D) case, altermagnetism is forbidden by the [C₂||cal T] symmetry, but it can emerge when such chains are stacked into a quasi-1D array. To generate altermagnetic spin splitting via this chain-stacking mechanism, two essential ingredients are required: a block-type spin order that spontaneously breaks the combined parity-time reversal symmetry, and finite inter-chain hopping. Using first-principles calculations, we identify the K₃Fe₂Se₄ family as a promising platform that realizes this mechanism, hosting a d-wave altermagnet even without lattice C₄ symmetry. Moreover, owing to its lower symmetry, the block-type folded chain exhibits an isotropic altermagnetic spin splitting, which may manifest as an altermagnetic wrapping effect. Our findings unify real-space block magnetism and reciprocal-space altermagnetism, establishing folded iron chains as a tunable platform for zero-moment spintronic applications.