The InfluxDB start-up script checks if the HTTP service is running by trying to connect to it. However, I have disabled HTTP in my configuration and use HTTPS. This behavior is also described on Github.
You can workaround this issue by adjusting the InfluxDB service configuration file (/etc/systemd/system/influxd.service). The commented out lines are old configuration and replaced by the used lines.
[Unit]
Description=InfluxDB is an open-source, distributed, time series database
Documentation=https://docs.influxdata.com/influxdb/
After=network-online.target
[Service]
User=influxdb
Group=influxdb
LimitNOFILE=65536
EnvironmentFile=-/etc/default/influxdb
ExecStart=/usr/bin/influxd -config /etc/influxdb/influxdb.conf $INFLUXD_OPTS
#ExecStart=/usr/lib/influxdb/scripts/influxd-systemd-start.sh
KillMode=control-group
Restart=on-failure
Type=simple
#Type=forking
PIDFile=
#PIDFile=/var/lib/influxdb/influxd.pid
[Install]
WantedBy=multi-user.target
Alias=influxd.service