Old question but there's a nice way of doing this at the moment.
$date = Carbon::parse('2018-08-01')->next('Monday');
Additionally, if you want to check if your date is monday first, you could do something like this:
$date = Carbon::parse(...);
// If $date is Monday, return $date. Otherwise, add days until next Monday.
$date = $date->is('Monday') ? $date : $date->next('Monday');
Or using the Carbon constants as suggested by @smknstd in the comment below:
$date = Carbon::parse(...);
// If $date is Monday, return $date. Otherwise, add days until next Monday.
$date = $date->is(Carbon::MONDAY) ? $date : $date->next(Carbon::MONDAY);
Carbon::now()->next(Carbon::MONDAY);
– Arbitrament