Key points Missense mutations in the gene encoding the α1 subunit of the skeletal muscle voltage‐gated Ca2+ channel induce type 1 hypokalaemic periodic paralysis, a poorly understood neuromuscular disease characterized by episodic attacks of paralysis associated with low serum K+. Acute expression of human wild‐type and R1239H HypoPP1 mutant α1 subunits in mature mouse muscles showed that R1239H fibres displayed Ca2+ currents of reduced amplitude and larger resting leak inward current increased by external acidification. External acidification also produced intracellular acidification at a higher rate in R1239H fibres and inhibited inward rectifier K+ currents. These data suggest that the R1239H mutation induces an elevated leak H+ current at rest flowing through a gating pore and could explain why paralytic attacks preferentially occur during the recovery period following muscle exercise. Abstract Missense mutations in the gene encoding the α1 subunit of the skeletal muscle voltage‐gated Ca2+ channel induce type 1 hypokalaemic periodic paralysis, a poorly understood neuromuscular disease characterized by episodic attacks of paralysis associated with low serum K+. The present study aimed at identifying the changes in muscle fibre electrical properties induced by acute expression of the R1239H hypokalaemic periodic paralysis human mutant α1 subunit of Ca2+ channels in a mature muscle environment to better understand the pathophysiological mechanisms involved in this disorder. We transferred genes encoding wild‐type and R1239H mutant human Ca2+ channels into hindlimb mouse muscle by electroporation and combined voltage‐clamp and intracellular pH measurements on enzymatically dissociated single muscle fibres. As compared to fibres expressing wild‐type α1 subunits, R1239H mutant‐expressing fibres displayed Ca2+ currents of reduced amplitude and a higher resting leak inward current that was increased by external acidification. External acidification also produced intracellular acidification at a higher rate in R1239H fibres and inhibited inward rectifier K+ currents. These data indicate that the R1239H mutation induces an elevated leak H+ current at rest flowing through a gating pore created by the mutation and that external acidification favours onset of muscle paralysis by potentiating H+ depolarizing currents and inhibiting resting inward rectifier K+ currents. Our results could thus explain why paralytic attacks preferentially occur during the recovery period following intense muscle exercise.