Никита

$date = [
    '10.04.2019',
    '11.04.2019',
    '12.04.2019',
    '13.04.2019',
    '14.04.2019',
    '15.04.2019',
    '16.04.2019',
    '17.04.2019',
    '18.04.2019'
];

$today = date('d.m.Y');
$date = array_slice($date, array_search($today, $date));
print_r($date);

/*
Array
(
    [0] => 15.04.2019
    [1] => 16.04.2019
    [2] => 17.04.2019
    [3] => 18.04.2019
)
*/