I've got the same problem : I'm building an alpine based docker image, and when I want to curl to a website of my organisation, this error appears. To solve it, I have to get the CA cert of my company, then, I have to add it to the CA certs of my image. Use OpenSSL to get the certificates related to the website :
openssl s_client -showcerts -servername my.company.website.org -connect my.company.website.org:443

This will output something like :
CONNECTED(00000005)
depth=2 CN = UbisoftRootCA
verify error:num=19:self signed certificate in certificate chain
...
-----BEGIN CERTIFICATE-----
...
-----END CERTIFICATE-----
-----BEGIN CERTIFICATE-----
... 
-----END CERTIFICATE-----
...

Get the last certificate (the content between the -----BEGIN CERTIFICATE----- and the
-----END CERTIFICATE----- markups included) and save it into a file (mycompanyRootCA.crt for example) Then, when you'll build your docker image from alpine, do the following :
FROM alpine
RUN apk add ca-certificates curl
COPY mycompanyRootCA.crt  /usr/local/share/ca-certificates/mycompanyRootCA.crt
RUN update-ca-certificates

Your image will now work properly!