We studied the effects of lactation stage and postpartum rate of increase of concentrate allowance on daily fermentable organic matter (FOM) intake, rumen papilla surface area, and fractional VFA absorption rate (k_aVFA). The concentrate treatment aimed to create a transient difference in daily FOM intake. Twelve rumen-cannulated, Holstein-Friesian cows had free access to either a dry period ration or a basal lactation ration. Starting at 4 DIM, concentrate allowance increased at a high (1.0 kg DM/d; HIGH, n = 6) or a low rate (0.25 kg DM/d; LOW, n = 6) up to a maximum of 10.9 kg DM/d. On sampling days (−50, −30, −10, 3, 9, 16, 30, 44, 60, and 80 DIM), the rumen contents were evacuated and papilla biopsies taken. Thereafter, k_aVFA was measured using the empty washed rumen technique with 46 L McDougall buffer (pH 6.0, 39°C), containing 120 mM VFA (60% acetic, 25% propionic, and 15% butyric acid) and a marker (Co-EDTA). From −50 to 3 DIM, FOM intake was 5.7 ± 0.3 kg/d (P = 0.29), papilla surface area decreased from 34.4 to 28.0 ± 2.0 mm² (P = 0.02) and k_aVFA decreased from 0.51 to 0.33 ± 0.03 /h (P < 0.01), with no differences between future treatment groups HIGH and LOW (P ≥ 0.33). From 3 to 80 DIM, FOM intake, papilla surface area, and k_aVFA increased to 15.0 ± 0.3 kg/d, 63.4 ± 2.0 mm², and 0.75 ± 0.03 /h respectively (all P < 0.01). A treatment by DIM interaction occurred for daily FOM intake (P < 0.01), which was greater in group HIGH at 16 DIM (12.3 vs. 10.1 ± 0.3 kg/d, P < 0.01), and for papilla surface area (P = 0.01), which was greater in group HIGH from 16 DIM (46.0 vs. 33.2 ± 2.0 mm², P < 0.01) through to 44 DIM (60.5 vs. 49.7 ± 2.0 mm², P = 0.01). However, a treatment by DIM interaction did not occur for k_aVFA (P = 0.28), which was similar for group HIGH and LOW at 16 DIM (0.60 vs. 0.56 ± 0.03 /h, P = 0.53) and 44 DIM (0.69 vs. 0.69 ± 0.03 /h, P = 0.95). In conclusion, lactation stage but not concentrate treatment affected k_aVFA. This suggests k_aVFA increases with, but is not limited by, papilla surface area during the first weeks of lactation, which was affected by the rate of increase of concentrate allowance.