Obstructive sleep apnoea (OSA) and type 2 diabetes frequently co‐exist and potentially interact haemodynamically and metabolically. However, the confounding effects of obesity have obscured the examination of any independent or interactive effects of the hypoxic stress of OSA and the hyperglycaemia of type 2 diabetes on haemodynamic and metabolic outcomes. We have developed a chronically catheterized, unhandled, lean murine model to examine the effects of intermittent hypoxic (IH) exposure and exogenous glucose infusion on the diurnal pattern of arterial blood pressure and blood glucose, as well as pancreatic β‐cell growth and function. Four experimental groups of adult male C57BL/J mice were exposed to 80 h of (1) either IH (nadir of inspired oxygen 5–6% at 60 cycles h⁻¹ for 12 h during light period) or intermittent air (IA; control) and (2) continuous infusion of either 50% dextrose or saline (control). IH exposure during saline infusion caused a sustained increase in arterial blood pressure of 10 mmHg (P < 0.0001), reversed the normal diurnal rhythm of blood glucose (P < 0.03), doubled corticosterone levels (P < 0.0001), and increased replication of pancreatic β‐cells from 1.5 ± 0.3 to 4.0 ± 0.8% bromodeoxyuridine (BrdU)‐positive) β‐cells. The combined stimulus of IH exposure and glucose infusion attenuated the hypertension, exacerbated the reversed diurnal glucose rhythm, and produced the highest rates of apoptosis in β‐cells, without any additive effects on β‐cell replication. We conclude that, in contrast to the development of sustained hypertension, IH impaired glucose homeostasis only during periods of hypoxic exposure. IH acted as a stimulus to pancreatic β‐cell replication, but the presence of hyperglycaemia may increase the hypoxic susceptibility of β‐cells. This model will provide a basis for future mechanistic studies as well as assessing the metabolic impact of common comorbities in OSA, including obesity, insulin resistance and type 2 diabetes.