I have seen a lot of posts about how you can do it with a date string but I am trying something for a dataframe column and haven't got any luck so far. My current method is : Get the weekday from 'myday' and then offset to get monday.

df['myday'] is column of dates. 
mydays = pd.DatetimeIndex(df['myday']).weekday
df['week_start'] = pd.DatetimeIndex(df['myday']) - pd.DateOffset(days=mydays)

But I get TypeError: unsupported type for timedelta days component: numpy.ndarray

How can I get week start date from a df column?

it fails because pd.DateOffset expects a single integer as a parameter (and you are feeding it an array). You can only use DateOffset to change a date column by the same offset.

try this :

import datetime as dt
# Change 'myday' to contains dates as datetime objects
df['myday'] = pd.to_datetime(df['myday'])  
# 'daysoffset' will container the weekday, as integers
df['daysoffset'] = df['myday'].apply(lambda x: x.weekday())
# We apply, row by row (axis=1) a timedelta operation
df['week_start'] = df.apply(lambda x: x['myday'] - dt.TimeDelta(days=x['daysoffset']), axis=1)

I haven't actually tested this code, (there was no sample data), but that should work for what you have described.

However, you might want to look at pandas.Resample, which might provide a better solution - depending on exactly what you are looking for.