An organic interposer includes dielectric material layers embedding redistribution interconnect structures, package-side bump structures located on a first side of the dielectric material layers, and die-side bump structures located on a second side of the dielectric material layers. A gap region is present between a first area including first die-side bump structures and a second area including second die-side bump structures. Stress-relief line structures are located on, or within, the dielectric material layers within an area of the gap region in the plan view. Each stress-relief line structures may include straight line segments that laterally extend along a respective horizontal direction and is not electrically connected to the redistribution interconnect structures. The stress-relief line structures may include the same material as, or may include a different material from, a metallic material of the redistribution interconnect structures or bump structures that are located at a same level.