Only a small fraction of massive stars seem to host a measurable structured magnetic field , whose origin is still unknown and whose implications for stellar evolution still need to be assessed . Within the context of the “ B fields in OB stars ( BOB ) ” collaboration , we used the HARPSpol spectropolarimeter to observe the early B-type stars \beta CMa ( HD 44743 ; B1 II/III ) and \epsilon CMa ( HD 52089 ; B1.5II ) in December 2013 and April 2014 . For both stars , we consistently detected the signature of a weak ( < 30 G in absolute value ) longitudinal magnetic field , approximately constant with time . We determined the physical parameters of both stars and characterise their X-ray spectrum . For the \beta Cep star \beta CMa , our mode identification analysis led to determining a rotation period of 13.6 \pm 1.2 days and of an inclination angle of the rotation axis of 57.6 \pm 1.7 ^ { \circ } , with respect to the line of sight . On the basis of these measurements and assuming a dipolar field geometry , we derived a best fitting obliquity of about 22 ^ { \circ } and a dipolar magnetic field strength ( B _ { \mathrm { d } } ) of about 100 G ( 60 < B _ { \mathrm { d } } < 230 G within the 1 \sigma level ) , below what is typically found for other magnetic massive stars . This conclusion is strengthened further by considerations of the star ’ s X-ray spectrum . For \epsilon CMa we could only determine a lower limit on the dipolar magnetic field strength of 13 G. For this star , we determine that the rotation period ranges between 1.3 and 24 days . Our results imply that both stars are expected to have a dynamical magnetosphere , so the magnetic field is not able to support a circumstellar disk . We also conclude that both stars are most likely core hydrogen burning and that they have spent more than 2/3 of their main sequence lifetime . A histogram of the distribution of the dipolar magnetic field strength for the magnetic massive stars known to date does not show the magnetic field “ desert ” observed instead for intermediate-mass stars . The biases involved in the detection of ( weak ) magnetic fields in massive stars with the currently available instrumentation and techniques imply that weak fields might be more common than currently observed . Our results show that , if present , even relatively weak magnetic fields are detectable in massive stars and that more observational effort is probably still needed to properly access the magnetic field incidence .