We present a high-sensitivity curvature and strain Mach–Zehnder interferometer (MZI) fiber sensor based on a configuration of no-core fiber (NCF) and four-core fiber (FCF). We used an optical fiber fusion splicer to directly splice a segment of FCF between two segments of NCF, with both the FCF and NCF made of SiO₂, where the FCF exhibits multi-path interference characteristics that allow for higher sensitivity. The NCF, with its self-focusing property, excites higher-order modes, which split and transmit it into the four cores of the FCF. The experimental results show that within a curvature range of 0.0104 m⁻¹–0.1515 m⁻¹, the maximum sensitivity can reach −78.04 dB/m⁻¹ with a high linear value of ~0.99. Additionally, the strain response is also experimentally studied. In the range of 0–600 με, the maximum strain sensitivity is −6.49 pm/με. The sensor demonstrates high curvature and strain sensitivity, indicating its potential applications in sensing measurements.