The effects of a quantitative feed restriction on the digestive physiology of the young rabbit remain largely unclear. Several digestive functions were thus analysed in the rabbit after weaning, using a monofactorial design that produces a linear reduction of the intake, from ad libitum (AL group) to 80%, 70% and 60% of AL (I80, I70 and I60). The restriction programme was applied by giving a daily meal during 21 days after weaning (34 days), and then a 4-day transition period was managed where the feed intake was fixed at 80% of the AL group, before to be fed ad libitum till 69 days of age. The young rabbit quickly adapted to the restriction programme, since within 4 days after weaning they ate totally their ration within 6–7 h after the feed distribution at 8:00, while AL animals consumed 75% of their feed between 15:00 and 8:00. From 55 to 59 days old, rabbits of I70 and I60 groups reached the intake of the I80 group within 1 day, and then the feed intake of restricted animals increased progressively without over-eating. From 54 to 69 days old, the intake of the four groups did not differ and averaged 143.7 g/day per rabbit. During restriction, the live weight and the weight gain decreased linearly with the restriction level. From 55 to 69 days, the weight gain increased linearly according to the restriction level previously applied, but the final weight of restricted rabbits remained lower than AL ones (−3%, −5% and −7%, respectively, for I80, I70 and I60). After 7 days of restriction, the digestibility was not significantly affected by the restriction level, except for crude protein that presented a slightly higher (+1.5 unit, P = 0.05) coefficient in I70 and I60 groups. The mean retention time (MRT) of particles increased by 50% for restricted animals (mean: 26.2 h for I80 and I60) compared to the AL ones, while that of the liquid phase (three times longer than the particles) was linearly and moderately increased with restriction (+20% between AL and I60). In restricted groups, the caecal pH was lower (−0.3 unit, P < 0.05) and could be related to their higher volatile fatty acid (VFA) concentration (+16 mmol/l compared to AL, P < 0.05). The fermentation pattern, ammonia concentration and the caecal bacterial fibrolytic activity remained similar among treatments, although the butyrate proportion tended to be higher in restricted animals. Impact of feed restriction on performances and digestive health is reported in the second part of this study.